The document discusses the International System of Units (SI). It states that the SI is the heir to the old metric decimal system, so it is also known generically as the metric system. One of the main characteristics of the International System of Units is that its units are based on fundamental physical phenomena. The units of the SI are the international reference for indications of all measuring instruments.
The International System of Units consists of seven basic units, also called fundamental units, which define the corresponding fundamental physical quantities that have been chosen by convention and allow any physical quantity to be expressed in terms of or as a combination of them. The fundamental physical quantities are complemented by two additional physical quantities called supplementary.
The document provides examples and exercises for converting between different units of measurement using the International System of Units (SI). It begins by showing how to convert between feet and meters. It then provides practice problems converting between units like kilometers, gallons, and miles. The document later discusses scientific notation and provides examples of converting values written in standard form to scientific notation. It also gives examples of converting between different temperature scales and units of time, length, mass and other quantities using conversion factors and dimensional analysis.
The document provides examples and exercises for converting between different units of measurement using the International System of Units (SI). It begins by showing how to convert between feet and meters. It then provides practice problems converting between units like kilometers, gallons, and miles. The document later discusses scientific notation and provides examples of converting values written in standard form to scientific notation. It also gives examples of converting between different temperature scales and units of time, length, mass and other quantities using conversion factors and dimensional analysis.
Introductory Physics - Physical Quantities, Units and MeasurementSutharsan Isles
This document provides an introduction to physical quantities, units, and measurement in physics. It begins with definitions of key terminology like physical property, scalar and vector quantities, and standard form notation. It then discusses the International System of Units (SI) including the seven base units, common prefixes, and how to convert between multiples and submultiples of units. The document also covers derived SI units and examples of converting between derived units. It emphasizes the importance of understanding whether a quantity is scalar or vector.
Many occupations require converting between metric units, including tradespeople, engineers, scientists, and medical professionals. It is easiest to use a conversion chart that shows relationships between units like kilometers, meters, centimeters, and millimeters. Area and volume conversions involve squaring or cubing the units, so they can produce very large results. Common area units include hectares and square meters, while volume is often measured in cubic meters, liters, or milliliters. Liquid volume is termed capacity. Mass conversions also use multiples of 1000, with the gram and kilogram as base units.
This document provides an overview of the AS Level Physics course and discusses key concepts related to physical quantities, including:
1. Physical quantities can be quantified by measurement and have units associated with them. There are two types: base quantities and derived quantities.
2. Base quantities are the seven SI base units: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Derived quantities are formed by mathematical relationships between base quantities.
3. When writing the units of a derived quantity, the formula is used to express the units in terms of the base units. Examples of deriving units for acceleration, force, and pressure are provided.
The document discusses the metric system of measurement. It explains that the metric system is based on a base unit and prefixes that are used to denote powers of ten. It provides the prefixes for the metric system and gives the base units and conversions for length, mass, and capacity. Examples are given for converting between metric units by moving the decimal point right or left based on the prefixes.
NCV 4 Mathematical Literacy Hands-On Support Slide Show - Module 1 Part 2Future Managers
The document provides information on measurements and units of measurement. It includes:
- Converting between different units like metres to kilometres
- Calculating speeds, rates, volumes and surface areas using formulas
- Measuring tools for different quantities like length, volume, mass
- Examples of calculating speeds, volumes, areas of different shapes
The document discusses the differences between the metric and standard/English systems of measurement. The metric system uses a base-10 system which makes conversions easier compared to the base-12 English system. Most countries use the metric system, with the only other country still using English being Myanmar. While the US still uses English measurements for convenience and cost reasons, the metric system is easier to use and is the universal standard for science. The document then explains the metric system prefixes and how to use them to convert between different metric units of measurement.
The document provides examples and exercises for converting between different units of measurement using the International System of Units (SI). It begins by showing how to convert between feet and meters. It then provides practice problems converting between units like kilometers, gallons, and miles. The document later discusses scientific notation and provides examples of converting values written in standard form to scientific notation. It also gives examples of converting between different temperature scales and units of time, length, mass and other quantities using conversion factors and dimensional analysis.
The document provides examples and exercises for converting between different units of measurement using the International System of Units (SI). It begins by showing how to convert between feet and meters. It then provides practice problems converting between units like kilometers, gallons, and miles. The document later discusses scientific notation and provides examples of converting values written in standard form to scientific notation. It also gives examples of converting between different temperature scales and units of time, length, mass and other quantities using conversion factors and dimensional analysis.
Introductory Physics - Physical Quantities, Units and MeasurementSutharsan Isles
This document provides an introduction to physical quantities, units, and measurement in physics. It begins with definitions of key terminology like physical property, scalar and vector quantities, and standard form notation. It then discusses the International System of Units (SI) including the seven base units, common prefixes, and how to convert between multiples and submultiples of units. The document also covers derived SI units and examples of converting between derived units. It emphasizes the importance of understanding whether a quantity is scalar or vector.
Many occupations require converting between metric units, including tradespeople, engineers, scientists, and medical professionals. It is easiest to use a conversion chart that shows relationships between units like kilometers, meters, centimeters, and millimeters. Area and volume conversions involve squaring or cubing the units, so they can produce very large results. Common area units include hectares and square meters, while volume is often measured in cubic meters, liters, or milliliters. Liquid volume is termed capacity. Mass conversions also use multiples of 1000, with the gram and kilogram as base units.
This document provides an overview of the AS Level Physics course and discusses key concepts related to physical quantities, including:
1. Physical quantities can be quantified by measurement and have units associated with them. There are two types: base quantities and derived quantities.
2. Base quantities are the seven SI base units: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Derived quantities are formed by mathematical relationships between base quantities.
3. When writing the units of a derived quantity, the formula is used to express the units in terms of the base units. Examples of deriving units for acceleration, force, and pressure are provided.
The document discusses the metric system of measurement. It explains that the metric system is based on a base unit and prefixes that are used to denote powers of ten. It provides the prefixes for the metric system and gives the base units and conversions for length, mass, and capacity. Examples are given for converting between metric units by moving the decimal point right or left based on the prefixes.
NCV 4 Mathematical Literacy Hands-On Support Slide Show - Module 1 Part 2Future Managers
The document provides information on measurements and units of measurement. It includes:
- Converting between different units like metres to kilometres
- Calculating speeds, rates, volumes and surface areas using formulas
- Measuring tools for different quantities like length, volume, mass
- Examples of calculating speeds, volumes, areas of different shapes
The document discusses the differences between the metric and standard/English systems of measurement. The metric system uses a base-10 system which makes conversions easier compared to the base-12 English system. Most countries use the metric system, with the only other country still using English being Myanmar. While the US still uses English measurements for convenience and cost reasons, the metric system is easier to use and is the universal standard for science. The document then explains the metric system prefixes and how to use them to convert between different metric units of measurement.
This document provides an overview of physical quantities and the International System of Units (SI) for measuring them. It defines physical quantities as things that can be measured with a magnitude and unit. The SI is standardized by the General Conference on Weights and Measures and uses seven base units: meter, kilogram, second, ampere, kelvin, candela, and mole. Derived quantities are defined in terms of base units, like speed being meters/second. Prefixes are used to modify units for very small or large numbers. The document gives examples of derived quantities and their units, like area being square meters.
This document contains two presentations about units of measurement. The first presentation defines various units used to measure quantities like length, mass, and volume. It also provides examples of converting between units like km, m, cm, and mm. The second presentation discusses upper and lower measurement bounds, explaining that measurements have some uncertainty and provide a range rather than an exact value. It gives an example, stating that a measurement of 12.7cm would have a lower bound of 12.65cm and upper bound of 12.75cm.
This document discusses units of measurement and conversions in physics. It introduces the International System of Units (SI) which standardizes the basic units used to measure length, mass, time, temperature, electric current, luminous intensity, and amount of substance. Derived units are also discussed, along with common prefixes used to denote powers of ten when measuring larger or smaller quantities. Examples are provided for unit conversions between kilometers and meters, and kilometers per hour and meters per second. The document also differentiates between accuracy and precision in measurements.
The document discusses measurement and conversions using the International System of Units (SI). It defines the base SI units for length, volume, mass, temperature and time. It also describes the common SI prefixes like kilo, hecto and milli used to indicate multiplication or division of the base units by powers of ten. Examples are provided to show how to convert between different units using the prefix multipliers.
The document discusses various standards of measurement used in science. It describes the metric system including common units of length, volume, mass, density, time, and temperature. For length, the basic metric unit is the meter. For volume, the basic unit is the liter. For mass, the basic unit is the kilogram. Density is a derived unit that represents mass per unit volume. Temperature is measured on the Kelvin scale in the SI system, with Celsius degrees also discussed.
The English system of measurement developed organically as people measured things using familiar objects from everyday life. Measurements varied between individuals until standards were established. The key units are:
- Length: 12 inches = 1 foot, 3 feet = 1 yard, 5280 feet = 1 mile
- Capacity: 3 teaspoons = 1 tablespoon, 16 tablespoons = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon
- Weight: 16 ounces = 1 pound, 2000 pounds = 1 ton
Conversions between units use proportional relationships, like 1 yard = 3 feet or 16 cups = 1 gallon.
This document discusses common units of measurement for length, weight, volume, and area. It provides conversion factors showing how to multiply or divide between units, such as the number of centimeters in a meter or grams in a kilogram. Examples are given demonstrating how to use the conversion factors to change between units of measure.
1. The document discusses various concepts related to measurement including length, area, volume, mass, density, and time. It describes the fundamental International System of Units (SI units) used to measure these physical quantities.
2. Methods for measuring length include using metre rules, tape measures, and estimating techniques. Area can be measured for regular shapes using formulas and irregular shapes can be divided into regular portions. Volume is measured using formulas for regular solids and displacement methods for irregular solids.
3. Mass is measured using balances, density is a ratio of mass to volume, and time intervals are recorded using stopwatches or clocks depending on the needed accuracy. Standardizing measurement systems and defining base SI units has allowed
The document discusses units and measurements in physics. It covers the metric and British systems of units, including standard units for length, mass, and time. The metric system is now the most widely used system, known as the International System of Units (SI). The SI base units are the meter, kilogram, and second. Conversion factors allow quantities to be expressed in different units while maintaining the same physical value. Unit analysis ensures quantities in equations have the same dimensions.
The metric system is the standard system of measurement used by scientists. It uses units like meters, liters, and grams to measure length, volume, mass, weight, density, and temperature. Conversion between units uses dimensional analysis and conversion factors that equal 1. Common metric units include meters for length, liters and milliliters for volume, grams and kilograms for mass, Newtons for weight, and Celsius degrees for temperature.
SIM ON CONVERSION OF LENGTH MEASUREMENTErnie Samson
This document provides information about converting between units in the metric system of measurement. It discusses the metric prefixes and metric conversion factors. It gives examples of converting between metric units by multiplying or dividing quantities by powers of 10, depending on whether the conversion is moving left or right on the metric system line. It includes practice problems for students to convert between metric units and solve word problems involving metric conversions.
This document provides information about the metric system of measurement including units of length, mass, and volume. It explains that the metric system is used in science for precise measurements and definitions. Key points include:
- The metric system uses prefixes like kilo, centi, and milli to denote powers of ten in units like meters, grams, and liters.
- Units of length are measured in meters (m) or centimeters (cm). Mass is measured in grams (g) or kilograms (kg). Volume is measured in liters (L) or milliliters (mL).
- Examples show converting between metric units using the prefixes and moving the decimal point based on powers of ten in
Measurement and units are important concepts in physics. The document discusses the SI system of units including fundamental units like meters, kilograms, and seconds. It also covers prefixes that are used with SI units to denote larger or smaller quantities. Derived units and dimensional analysis are introduced. The document also discusses measurement precision, significant figures, scientific notation, and estimating order of magnitude. Calculating with measurements and expressing uncertainty are also summarized.
The document discusses converting between centimeters and meters by multiplying or dividing by 100. To convert from centimeters to meters, one divides the measurement in centimeters by 100 and moves the decimal point two places to the left. To convert from meters to centimeters, one multiplies the measurement in meters by 100 and moves the decimal point two places to the right. Examples are provided of converting various measurements between centimeters and meters.
Standards of measurement require agreed upon units for comparison. The International System of Units (SI) is the standard system used by most nations, with base units for length, mass, time, and other quantities. SI units include the meter for length, kilogram for mass, second for time, and kelvin for temperature. The appropriate unit depends on the size of the item measured, with smaller objects often measured in centimeters, grams or other decimal units.
This document provides information about using the metric system, including identifying appropriate metric units for mass, capacity, and length. It gives examples and reference amounts for different metric units. It also discusses converting between metric units by multiplying or dividing by powers of ten based on the relative sizes of the units.
This document discusses physical quantities and units in physics. It defines a physical quantity as something that can be measured, like length, weight, or time, and notes that every physical quantity has a magnitude and unit. It discusses unit conversion for areas and volumes using prefixes like milli (10-3). Base units include meters, kilograms, and seconds. Derived units are combinations of base units and must be multiplied or divided, not added or subtracted. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction, and can be represented by arrows. Methods for adding and resolving vectors are also outlined.
The document discusses the International System of Units (SI). It states that the SI is the heir to the old metric decimal system, so it is also known generically as the metric system. One of the main characteristics of the International System of Units is that its units are based on fundamental physical phenomena. The units of the SI are the international reference for indications of all measuring instruments.
The International System of Units consists of seven basic units, also called fundamental units, which define the corresponding fundamental physical quantities. These have been chosen by convention and allow any physical quantity to be expressed in terms of them or as a combination of them. Two additional physical quantities are supplemented.
[/SUMMARY]
This document discusses units and measurements in science. It defines fundamental and derived quantities and identifies the base SI units for length, mass, time, temperature and other quantities. It also explains prefixes used in the metric system and how to convert between units. Measurement tools for length, volume, temperature are also introduced. The importance of accuracy and precision in scientific measurements is emphasized.
The document discusses physics and chemistry, comparing what they have in common (studying matter) and what makes them different (physics studies phenomena that don't change matter composition, while chemistry studies phenomena that do change composition). It then provides an overview of the scientific method, including making observations and asking questions, developing hypotheses to test, conducting controlled experiments, analyzing results, and drawing conclusions. Finally, it covers scientific concepts like units, measurements, errors, and notation.
JEE Main 11&12 Sample ebook, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
This document provides an overview of physical quantities and the International System of Units (SI) for measuring them. It defines physical quantities as things that can be measured with a magnitude and unit. The SI is standardized by the General Conference on Weights and Measures and uses seven base units: meter, kilogram, second, ampere, kelvin, candela, and mole. Derived quantities are defined in terms of base units, like speed being meters/second. Prefixes are used to modify units for very small or large numbers. The document gives examples of derived quantities and their units, like area being square meters.
This document contains two presentations about units of measurement. The first presentation defines various units used to measure quantities like length, mass, and volume. It also provides examples of converting between units like km, m, cm, and mm. The second presentation discusses upper and lower measurement bounds, explaining that measurements have some uncertainty and provide a range rather than an exact value. It gives an example, stating that a measurement of 12.7cm would have a lower bound of 12.65cm and upper bound of 12.75cm.
This document discusses units of measurement and conversions in physics. It introduces the International System of Units (SI) which standardizes the basic units used to measure length, mass, time, temperature, electric current, luminous intensity, and amount of substance. Derived units are also discussed, along with common prefixes used to denote powers of ten when measuring larger or smaller quantities. Examples are provided for unit conversions between kilometers and meters, and kilometers per hour and meters per second. The document also differentiates between accuracy and precision in measurements.
The document discusses measurement and conversions using the International System of Units (SI). It defines the base SI units for length, volume, mass, temperature and time. It also describes the common SI prefixes like kilo, hecto and milli used to indicate multiplication or division of the base units by powers of ten. Examples are provided to show how to convert between different units using the prefix multipliers.
The document discusses various standards of measurement used in science. It describes the metric system including common units of length, volume, mass, density, time, and temperature. For length, the basic metric unit is the meter. For volume, the basic unit is the liter. For mass, the basic unit is the kilogram. Density is a derived unit that represents mass per unit volume. Temperature is measured on the Kelvin scale in the SI system, with Celsius degrees also discussed.
The English system of measurement developed organically as people measured things using familiar objects from everyday life. Measurements varied between individuals until standards were established. The key units are:
- Length: 12 inches = 1 foot, 3 feet = 1 yard, 5280 feet = 1 mile
- Capacity: 3 teaspoons = 1 tablespoon, 16 tablespoons = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon
- Weight: 16 ounces = 1 pound, 2000 pounds = 1 ton
Conversions between units use proportional relationships, like 1 yard = 3 feet or 16 cups = 1 gallon.
This document discusses common units of measurement for length, weight, volume, and area. It provides conversion factors showing how to multiply or divide between units, such as the number of centimeters in a meter or grams in a kilogram. Examples are given demonstrating how to use the conversion factors to change between units of measure.
1. The document discusses various concepts related to measurement including length, area, volume, mass, density, and time. It describes the fundamental International System of Units (SI units) used to measure these physical quantities.
2. Methods for measuring length include using metre rules, tape measures, and estimating techniques. Area can be measured for regular shapes using formulas and irregular shapes can be divided into regular portions. Volume is measured using formulas for regular solids and displacement methods for irregular solids.
3. Mass is measured using balances, density is a ratio of mass to volume, and time intervals are recorded using stopwatches or clocks depending on the needed accuracy. Standardizing measurement systems and defining base SI units has allowed
The document discusses units and measurements in physics. It covers the metric and British systems of units, including standard units for length, mass, and time. The metric system is now the most widely used system, known as the International System of Units (SI). The SI base units are the meter, kilogram, and second. Conversion factors allow quantities to be expressed in different units while maintaining the same physical value. Unit analysis ensures quantities in equations have the same dimensions.
The metric system is the standard system of measurement used by scientists. It uses units like meters, liters, and grams to measure length, volume, mass, weight, density, and temperature. Conversion between units uses dimensional analysis and conversion factors that equal 1. Common metric units include meters for length, liters and milliliters for volume, grams and kilograms for mass, Newtons for weight, and Celsius degrees for temperature.
SIM ON CONVERSION OF LENGTH MEASUREMENTErnie Samson
This document provides information about converting between units in the metric system of measurement. It discusses the metric prefixes and metric conversion factors. It gives examples of converting between metric units by multiplying or dividing quantities by powers of 10, depending on whether the conversion is moving left or right on the metric system line. It includes practice problems for students to convert between metric units and solve word problems involving metric conversions.
This document provides information about the metric system of measurement including units of length, mass, and volume. It explains that the metric system is used in science for precise measurements and definitions. Key points include:
- The metric system uses prefixes like kilo, centi, and milli to denote powers of ten in units like meters, grams, and liters.
- Units of length are measured in meters (m) or centimeters (cm). Mass is measured in grams (g) or kilograms (kg). Volume is measured in liters (L) or milliliters (mL).
- Examples show converting between metric units using the prefixes and moving the decimal point based on powers of ten in
Measurement and units are important concepts in physics. The document discusses the SI system of units including fundamental units like meters, kilograms, and seconds. It also covers prefixes that are used with SI units to denote larger or smaller quantities. Derived units and dimensional analysis are introduced. The document also discusses measurement precision, significant figures, scientific notation, and estimating order of magnitude. Calculating with measurements and expressing uncertainty are also summarized.
The document discusses converting between centimeters and meters by multiplying or dividing by 100. To convert from centimeters to meters, one divides the measurement in centimeters by 100 and moves the decimal point two places to the left. To convert from meters to centimeters, one multiplies the measurement in meters by 100 and moves the decimal point two places to the right. Examples are provided of converting various measurements between centimeters and meters.
Standards of measurement require agreed upon units for comparison. The International System of Units (SI) is the standard system used by most nations, with base units for length, mass, time, and other quantities. SI units include the meter for length, kilogram for mass, second for time, and kelvin for temperature. The appropriate unit depends on the size of the item measured, with smaller objects often measured in centimeters, grams or other decimal units.
This document provides information about using the metric system, including identifying appropriate metric units for mass, capacity, and length. It gives examples and reference amounts for different metric units. It also discusses converting between metric units by multiplying or dividing by powers of ten based on the relative sizes of the units.
This document discusses physical quantities and units in physics. It defines a physical quantity as something that can be measured, like length, weight, or time, and notes that every physical quantity has a magnitude and unit. It discusses unit conversion for areas and volumes using prefixes like milli (10-3). Base units include meters, kilograms, and seconds. Derived units are combinations of base units and must be multiplied or divided, not added or subtracted. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction, and can be represented by arrows. Methods for adding and resolving vectors are also outlined.
The document discusses the International System of Units (SI). It states that the SI is the heir to the old metric decimal system, so it is also known generically as the metric system. One of the main characteristics of the International System of Units is that its units are based on fundamental physical phenomena. The units of the SI are the international reference for indications of all measuring instruments.
The International System of Units consists of seven basic units, also called fundamental units, which define the corresponding fundamental physical quantities. These have been chosen by convention and allow any physical quantity to be expressed in terms of them or as a combination of them. Two additional physical quantities are supplemented.
[/SUMMARY]
This document discusses units and measurements in science. It defines fundamental and derived quantities and identifies the base SI units for length, mass, time, temperature and other quantities. It also explains prefixes used in the metric system and how to convert between units. Measurement tools for length, volume, temperature are also introduced. The importance of accuracy and precision in scientific measurements is emphasized.
The document discusses physics and chemistry, comparing what they have in common (studying matter) and what makes them different (physics studies phenomena that don't change matter composition, while chemistry studies phenomena that do change composition). It then provides an overview of the scientific method, including making observations and asking questions, developing hypotheses to test, conducting controlled experiments, analyzing results, and drawing conclusions. Finally, it covers scientific concepts like units, measurements, errors, and notation.
JEE Main 11&12 Sample ebook, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
JEE Main Advanced 11 Sample ebook, which helps you to understand the chapter in easy way also download sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
JEE Main Advanced 11 & 12th Sample ebookMiso Study
JEE Main Advanced 11 & 12th Sample ebook, which helps you to understand the chapter in easy way also download sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
Units are necessary in physics to measure physical quantities and enable consistent comparisons. There are two types of units - fundamental units which measure fundamental quantities like length, mass, and time, and derived units which measure derived quantities like area, speed, and force. The International System of Units (SI) defines seven base units, including the meter, kilogram, and second. Units are also defined for other physical quantities using prefixes to indicate multiples or submultiples of the base units, enabling measurement of a wide range of quantities. Proper choice of units allows for convenient measurement depending on the magnitude of the physical quantity.
The metric system was created in 1790 by the French Academy of Sciences to provide a consistent standard of measurement. It set the meter as the base unit of length, derived other units from it, and organized them into a decimal system with prefixes denoting powers of ten. The metric system, also known as the International System of Units, or SI, was adopted to provide a modern, simple, and scientific standard that was easy to use across borders.
This document discusses physical quantities, units, dimensions, and measurement. It can be summarized as follows:
1) A physical quantity is something that can be measured, like length, mass, time, etc. It has a magnitude and unit. Measurement allows determining the magnitude of a physical quantity and comparing similar quantities.
2) There are three main systems of units - CGS, MKS, and SI. The SI system has seven base units including the meter, kilogram, and second. Prefixes are used to denote multiples and submultiples of units for very large or small quantities.
3) Standards have been established for the meter, kilogram, and second based on properties of light and atoms
The document discusses measurement, calibration, and units of measurement. Some key points:
- Measurement is the first step to control and improvement. If you can't measure something, you can't understand or control it.
- The International System of Units (SI) defines seven base units including the meter, kilogram, second, ampere, kelvin, mole, and candela. Other units are derived from these base units.
- Calibration establishes the relationship between measurement instruments and reference standards under specific conditions. Regular calibration helps ensure accuracy and traceability to national standards.
- Factors like instrument specifications, use, environment, and measurement accuracy needed should be considered when determining calibration frequency.
06 Ps300 Making Measurements & Using The Metric System Notes Keplenning
This document provides an overview of measurement and the metric system. It defines key terms like qualitative vs. quantitative observations, precision vs. accuracy, and base SI units for length, mass, volume, and time. It explains how to use tools like rulers, balances, and thermometers to make measurements. It also covers converting between metric units using factors and moving the decimal place.
This document provides an overview of key concepts from Chapter 3 on scientific measurement, including:
1) It discusses the importance of measurements and units in science, introducing the International System of Units (SI) with base units like meters, kilograms, and seconds.
2) It covers the concepts of accuracy, precision, and errors in measurement, as well as significant figures and proper reporting of measurements.
3) The document outlines methods for unit conversion using dimensional analysis and conversion factors to solve multi-step problems.
This document provides an introduction to basic mathematical concepts for chemistry and physics, including units of measurement and conversion, proportionality, and equations of the first and second degree. It covers scalar and vector quantities, the International System of Units (SI) and its fundamental and derived units, scientific notation, proportionality, and how to solve linear and quadratic equations. The goal is to review key mathematical concepts that are frequently used in solving physics and chemistry problems in the first year of an odontology degree program.
This document provides an overview of key concepts in chemistry including:
1. It introduces significant figures and the rules for determining how many figures are meaningful in measurements and calculations.
2. It describes the scientific method as a cycle of making observations, forming hypotheses, designing experiments to test hypotheses, and using results to develop theories or laws.
3. It outlines the metric system and prefixes used to modify base units of measurement like grams, meters, and liters.
This document discusses the International System of Units (SI), which is the standard system of measurement used internationally, especially in science. It notes that SI provides a coherent and rationalized system of measurements based around powers of ten. Key aspects of SI include standardized prefixes that indicate multiplicative factors of units and a unified system of measuring length, mass and volume. SI aims to make scientific measurements easily understood worldwide.
1) The document discusses the importance of quantification and measurement in physics, describing how all physical phenomena can be described numerically.
2) It introduces systems of units for measurement, including fundamental and derived units, and discusses the International System of Units (SI).
3) Examples are provided for adding, subtracting, multiplying and dividing quantities with the appropriate units. Conversions between different units are also demonstrated.
This document discusses measurement units and systems. It covers:
1) Physical quantities that can be measured like length have corresponding units like meters. The International System of Units (SI) provides standard agreed units.
2) Base quantities like mass and time have fundamental SI units like kilograms and seconds. Derived quantities are expressed in terms of base quantities.
3) Prefixes are used to denote multiples of units, e.g. kilo for 1000. Dimensional analysis ensures quantities in equations have the same physical dimensions.
This document discusses scientific measurement and units. It covers accuracy, precision, and error in measurements. It introduces the International System of Units (SI) including the base units for length, volume, mass, temperature, and energy. It discusses significant figures and proper handling of calculations and conversions between units using dimensional analysis and conversion factors.
1. Measurements are necessary for experiments, production, and quality control. Standard units are needed to make measurements reliable, accurate, and uniform for all.
2. The CGS, MKS, and SI systems define standard units for measurements of length, mass, and time. The SI system is now accepted internationally.
3. Accuracy refers to how close a measurement is to the true value, while precision refers to the consistency of repeated measurements. Errors are the differences between measured and actual values.
This document discusses various topics related to units and measurement including:
- Physical quantities that are fundamental or derived and their corresponding units
- Characteristics of standard units and different systems of units like SI, fps and cgs
- Definitions of fundamental SI units like meter, kilogram, second, etc.
- Methods of measuring length at different scales from micrometers to astronomical distances
- Measurement of other quantities like mass and time
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Este documento presenta información sobre las proteínas y sus componentes básicos como los aminoácidos y péptidos. Explica que los aminoácidos son las unidades que forman las proteínas al unirse mediante enlaces peptídicos. Describe los diferentes tipos de aminoácidos y su clasificación. También cubre temas como la estructura primaria de las proteínas, el código genético y la traducción de los mensajes de ARN en proteínas.
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detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
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International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
2. El Sistema Internacional de Unidades, abreviado S.I.,
también denominado Sistema Internacional de
Medidas, es el heredero del antiguo sistema métrico
decimal, por lo que el S.I. también es conocido de
forma genérica como sistema métrico.
Una de las principales características del Sistema
Internacional de Medidas es que sus unidades están
basadas en fenómenos físicos fundamentales. Las
unidades del S.I. son la referencia internacional de las
indicaciones de todos los instrumentos de medida, y a
las que están referidas a través de una cadena
ininterrumpida de calibraciones o comparaciones.
INTRODUCCIÓN
3. El Sistema Internacional de Unidades consta de siete unidades básicas, también
denominadas unidades fundamentales, que definen a las correspondientes
magnitudes físicas fundamentales, que han sido elegidas por convención, y que
permiten expresar cualquier magnitud física en términos o como combinación
de ellas. Las magnitudes físicas fundamentales se complementan con dos
magnitudes físicas más, denominadas suplementarias.
4. ¿PARA QUE SE USAN LAS
MEDIDAS?
LA QUÍMICA es la ciencia experimental
que estudia LA MATERIA y sus
transformaciones, conjuntamente con
sus propiedades.
MATERIA es todo aquello que tiene
masa y volumen (es decir todo
aquello que ocupa un lugar en el
espacio). Por consiguiente, LA MASA
y EL VOLUMEN son propiedades
generales de la materia.
Se usan LAS MEDIDAS para cuantificar las propiedades
de la materia.
LOS MATERIALES son las
diversas formas físicas
en que la materia se
presenta.
LA MATERIA es todo lo que nos rodea.
5. Las unidades de medida no pueden elegirse de forma arbitraria
debido a las leyes físicas que las vinculan unas con otras
6. ¿QUÉ ES MEDIR?
ES DETERMINAR LA CANTIDAD
O VALOR DE UNA PROPIEDAD
FÍSICA DE LA MATERIA,
LLAMADA MAGNITUD.
¿QUÉ ES MAGNITUD?
ES TODO AQUELLO QUE
PUEDE SER MEDIDO.
MEDIDA DE UNA MAGNITUD:
CANTIDAD + UNIDAD
150 Km
METROLOGÍA
Etimología de la palabra (griego):
METRON = medida
LOGOS = tratado
¿Desde cuando existe?
Génesis 6:15“ ....... y haz de fabricarla de
esta suerte :
la longitud del arca será de trescientos
codos, la anchura de cincuenta codos y de
treinta codos su altura.”
Levítico 19, 35-36 “......... No cometáis injusticias en los
juicios, ni en las medidas de longitud, peso o de
capacidad; usen balanza justa, peso, medidas y
sextuáreo justo”
Nuestros antepasados
medían el tiempo con el
sol y la luna
7. Uso Común de medidas
Cerca - lejos
Rápido o
Lento
Pesado
Liviano
Silencio - Ruido Frío - caliente
8. TIPOS DE MAGNITUDES
FUNDAMENTALES: Aquellas que
se determinan directamente con
un proceso de medición.
DERIVADAS: Aquellas que se determinan
a partir de otras medidas fundamentales.
UNIDADES
Las unidades son las referencias
o patrones con respecto a los
cuales se compara una medida
Están establecidas por convenio.
Deben ser constantes: no han de
cambiar según el individuo que haga
la medida o a lo largo del tiempo.
Deben ser universales: no
han de cambiar de unos
países a otros.
Han de ser fáciles de reproducir, aunque esta
facilidad vaya, a veces, en detrimento de la
exactitud.
9. ¿Qué es la cantidad
de una medición?
Es el dato numérico que representa
la comparación de magnitudes, es el
valor de la magnitud a la cual se esta
midiendo.
Por ejemplo:
Las dimensiones como: la masa (m) el tiempo
(t) la longitud (L) y la temperatura (T) se
conocen como dimensiones primarias o
fundamentales.
Existen también otras dimensiones como la
velocidad (v), energía (E) y el volumen (V), que se
expresan en términos compuestos por dimensiones
primarias y se les denomina dimensiones
secundarias o dimensiones derivadas.
10. SISTEMA INTERNACIONAL DE UNIDADES S.I
El Sistema Internacional de Unidades consta de
siete unidades básicas, también denominadas
unidades fundamentales. Son las unidades
utilizadas para expresar las magnitudes físicas
definidas como fundamentales, a partir de las
cuales se definen las demás.
Fue creado en 1960 por la
Conferencia General de Pesas y
Medidas, que inicialmente definió
seis unidades físicas básicas o
fundamentales. En 1971, fue
añadida la séptima unidad básica,
el mol.
Antecedentes del
SI
Sistema Métrico Decimal
Sistema Cegesimal (CGS)
Sistema MKS
(Sistema Giorgi)
Sistema Internacional de
Unidades
1899
1874
1901
1960
libra/pie/seg
12. Magnitud Nombre Símbolo
Superficie metro2 m2
Volumen metro3 m3
Velocidad metro / segundo m/ s
Aceleración metro / segundo2 m/s2
Número de ondas metro-1 m-1
Masa en volumen kilogramo/metro3 kg/m3
Velocidad angular radián/ segundo rad/s
Aceleración angular radián / segundo2 rad/s2
Unidades Derivadas
13. Magnitud Nombre Símbolo
Expresión en
unidades S.I
básicas
Frecuencia hertz Hz s-1
Fuerza newton N kg∙ m/s2
Presión Pascal Pa
kg/m1∙s2
Energía Joule J kg∙m2/s2
Potencia Watt W kg∙m2/s3
Carga eléctrica Coulomb C s∙A
Resistencia eléctrica Ohm W kg∙m2/s3∙A
Unidades Derivadas con nombre y símbolos especiales.
14. Uso de la coma (,):
CORRECTO: 345,7 m INCORRECTO: 345.7 m
Reglas de escritura del SI
15. Uso del espacio
CORRECTO INCORRECTO
5 678 200 m 5,678200 m
0,025 7 m 0.0257 m
Reglas de escritura del SI
16. Reglas de escritura del SI
CORRECTO INCORRECTO
0,7 m o,7 m
$50,00 $50,oo
Escribir con caracteres regulares y homogéneos
17. Reglas de escritura del SI
No combinar unidades del SI con unidades de
otros sistemas cuando se expresan
magnitudes.
CORRECTO INCORRECTO
Km/L Km/gal
18. Reglas de escritura del SI
Los símbolos de las unidades deben de
escribirse con minúscula excepto las que se
derivan de nombres propios.
UNIDAD CORRECTO INCORRECTO
metro m M ó mtr.
segundo s S ó seg.
ampère A Amp.
pascal Pa Pa ó Pas.
19. Reglas de escritura del SI
Utilizar signos de puntuación
solo en casos necesarios
CORRECTO INCORRECTO
33,2 m 33,2-m
40,2 kg 40,2.kg
Entre la cantidad y el símbolo,
dejar un espacio vacío, sin ningún gráfico
20. Reglas de escritura del SI
No usar siglas o iniciales como
símbolos de unidades
CORRECTO INCORRECTO
2 cm³ 2 cc
16 m/s 16 m.p.s
21. Reglas de escritura del SI
Los símbolos de las unidades se escriben en
singular indistintamente del valor de la
cantidad expresada
CORRECTO INCORRECTO
0,06 m 0,06 ms
66,5 g 66,5 gs
22. CONVERSIÓN DE UNIDADES
Permite expresar una cantidad en
términos de otras unidades sin alterar su
valor ni su magnitud física.
FACTOR DE CONVERSIÓN: Es la expresión de
una cantidad con sus respectivas unidades,
que es usada para convertirla en su
equivalente en otras unidades de medida
establecidas en dicho factor.
23.
24. ¿Como convertir unidades?
Ejemplo:
Convertir 540 m a cm
Solución
1. Identificamos la unidad de partida y la unidad
de destino (donde debemos llegar).
Escribe la conversión en forma de fracción
Multiplica
Cancela unidades arriba y abajo
El ejemplo nos indica que debemos expresar
m (metros) en cm (centímetros).
2. Identificamos la equivalencia
1 m = 100 cm
Podemos expresarla en forma de fracción, según
sea el caso que nos demande utilizar
1 𝑚
100 𝑐𝑚
100 𝑐𝑚
1 𝑚
ó
3. Escribimos el valor que nos piden convertir,
multiplicado por su respectiva equivalencia.
Pero …
¿Cuál de las
dos utilizo?
Se utiliza el factor (fracción) que
cancele la unidad de partida y
conserve la unidad de destino.
540 𝑚 ×
?
?
540 𝑚 ×
100 𝑐𝑚
1 𝑚
La unidad que se desea cancelar
deberá estar en el denominador.
540 𝑚 ×
100 𝑐𝑚
1 𝑚
= 54 000 𝑐𝑚
Respuesta
25. Para resolver: La distancia que hay del home al jardín central de un campo de béisbol es
de 400 pies (ft), convierta esta cantidad a metros.
Solución
1. Identificamos la unidad de partida y la unidad
de destino (donde debemos llegar).
El ejemplo nos indica que debemos expresar
ft (pies) en m (metros).
2. Identificamos la equivalencia
1 m = 3,28 ft
3. Escribimos el valor que nos piden convertir,
multiplicado por su respectiva equivalencia
400 𝑓𝑡 ×
1 𝑚
3,28 𝑓𝑡
= 121,95 𝑚
Respuesta
Para practicar:
Convertir 6 Km a pies
Convertir 7 galones a centímetros cúbicos
Convertir 100 millas a Km
26. Convertir 6 Km a pies
Convertir 7 galones a centímetros cúbicos
Convertir 100 millas a Km
SOLUCIÓN
27. 80
𝐾𝑚
ℎ
×
1000 𝑚
1 𝐾𝑚
×
1 ℎ
60 𝑚𝑖𝑚
×
1 𝑚𝑖𝑛
60 𝑠
= 22,22 𝑚/𝑠
¿Como convertir unidades?
Ejemplo:
Convertir 80 Km/h a m/s
Solución
1. Identificamos la unidad de partida y la unidad
de destino (donde debemos llegar).
Escribe la conversión en forma de fracción
Multiplica
Cancela unidades arriba y abajo
El ejemplo nos indica que debemos expresar
Km/h (kilómetros por hora) en m/s (metros por
segundo).
2. Identificamos las equivalencias
1 Km = 1000 m
1 h = 60 min
1 min = 60 s
Podemos expresarla en forma de fracción, según sea el
caso que nos demande utilizar
1 𝐾𝑚
1000 𝑚
ó
3. Escribimos el valor que nos piden convertir,
multiplicado por su respectiva equivalencia.
Pero …
¿Cuál de las
dos utilizo?
Se utiliza el factor (fracción) que
cancele las unidades de partida y
conserve las unidades de destino.
80
𝐾𝑚
ℎ
×
?
?
×
?
?
80
𝐾𝑚
ℎ
×
1000 𝑚
1 𝐾𝑚
×
1 ℎ
60 𝑚𝑖𝑚
×
1 𝑚𝑖𝑛
60 𝑠
Las unidades que se desean cancelar
deberán estar en el denominador y
numerador, según corresponda.
Respuesta
1 ℎ
60 𝑚𝑖𝑚
1 𝑚𝑖𝑛
60 𝑠
1000 𝑚
1 𝐾𝑚
60 𝑚𝑖𝑛
1 ℎ
60 𝑠
1 𝑚𝑖𝑛
28. Para resolver: Un automóvil se desplaza a una velocidad de 20 m/s. Expresar dicha velocidad
en Km/h
Solución
1. Identificamos la unidad de partida y la unidad
de destino (donde debemos llegar).
El ejemplo nos indica que debemos expresar m/s
(metros por segundo) en Km/h (kilómetros por
hora)
2. Identificamos la equivalencia
3. Escribimos el valor que nos piden convertir,
multiplicado por su respectiva equivalencia
Respuesta
Para practicar:
Convertir 2500 L/s a m3/h
Convertir 50 mL/min a L/s
Convertir 800 g/cm3 a Kg/m3
1 Km = 1000 m
1 h = 60 min
1 min = 60 s
20
𝑚
𝑠
×
1 𝐾𝑚
1 000 𝑚
×
60 𝑠
1 𝑚𝑖𝑚
×
60 𝑚𝑖𝑛
1 ℎ
= 79,2 𝐾𝑚/ℎ
30. Las potencias son una manera abreviada
de escribir una multiplicación formada por
varios números iguales. Son muy útiles
para simplificar multiplicaciones donde se
repite el mismo número.
Las potencias están formadas por la
base y por el exponente. La base es
el número que se está multiplicando
varias veces y el exponente es el
número de veces que se multiplica la
base.
¿qué son y para
qué sirven?
POTENCIAS
31. ¿Qué es la base?
Es el número que se está
multiplicando. ¿Qué es el exponente?
Las veces que se repite el
número.
¿Cómo se forma una potencia?
Se disponen de la siguiente
manera: el número de la base de
escribe de forma normal, y el
número de la potencia se escribe
más pequeño que la base en la
parte superior derecha.
32. Potencias de exponente natural
Una potencia es una forma abreviada de escribir un producto de varios
factores iguales.
BASE
EXPONENTE
𝑎 × 𝑎 × 𝑎 × 𝑎 × 𝑎 = 𝑎5
Ejemplo: La potencia de base 3 y exponente 5 es:
35 = 3 x3 x3 x3 x3 = 243
EXPONENTE
BASE
35
33.
34. Propiedades de las potencias de exponente natural
Cociente de potencias de la misma base
Si dividimos dos potencias de la misma base, el
resultado es otra potencia de la misma base cuyo
exponente es igual a la diferencia de los
exponentes.
an : am = = an – m
con n > m
m
a
an
35
32
3x3
3x3x3x3x3
33
Potencia de un producto
(a·b)n = an ·bn
Potencia de una potencia
Si elevamos una potencia a un
nuevo exponente, el resultado es
otra potencia con la misma base
cuyo exponente es el producto
de los exponentes.
23
2
26
(an)m = an · m
Producto de potencias de la misma base
Si multiplicamos dos potencias de la misma base,
el resultado es otra potencia de la misma base cuyo
exponente es la suma de los exponentes.
32 x 34 = 36
an · am = an +m
35. 1. Potencias de exponente negativo
Vamos a dar significado a la expresión a–n, que es una potencia en la que
el exponente es un número negativo. También a la expresión a0, en la que
el exponente es 0. Para ello, utilizamos la propiedad del cociente de
potencias de la misma base.
Aplicando la definición
de potencia y
simplificando
Aplicando la propiedad del
cociente de potencias de
igual base
Si los dos resultados han
de ser iguales debe ser:
35
33333
34
3333
3
35
54
1
34 3 3 31
3
34
3333
1
34
3333
34
44 0
3 3
34 30
1
33
333
1
35
33333 32
33
35
2
35 3 3 32
1
32
36. Las potencias de exponente entero se definen así:
► an = a . a . a . ... . a, para n natural y mayor que 1.
► a1 = a
► a0 = 1
para n natural y n > 0
► a–n = 1
an
Los ejemplos anteriores nos permite darnos cuenta de que es
necesario definir las potencias de exponente negativo (que ya no
consisten en multiplicar un número por sí mismo) de manera que
además sigan cumpliendo las propiedades que ya conocemos.
37. NOTACIÓN CIENTÍFICA
La notación científica nos permite escribir
números muy grandes o muy pequeños de
forma abreviada. Esta notación consiste
simplemente en multiplicar por una
potencia de base 10 con exponente
positivo o negativo.
La notación científica (o notación índice estándar) es una manera rápida de
representar un número utilizando potencias de base diez. Esta notación se
utiliza para poder expresar fácilmente números muy grandes o muy pequeños
Existen numerosos contextos donde
aparecen números muy grandes o
muy pequeños. Las masas de los
astros, las distancias interestelares…
son cantidades muy grandes; el
peso de los átomos, el diámetro de
un glóbulo rojo… son cantidades
muy pequeñas.
38. ¿Para que sirve?
La notación científica se desarrolló para
ayudar a los matemáticos y científicos para
expresar y trabajar con números muy
grandes y muy pequeños.
Existen numerosos contextos
donde aparecen números muy
grandes o muy pequeños. Las
masas de los astros, las
distancias interestelares… son
cantidades muy grandes; el peso
de los átomos, el diámetro de un
glóbulo rojo… son cantidades
muy pequeñas.
39. Un número en notación científica N = a,bcd... . 10n consta de:
• Una parte entera formada por una sólo cifra: a
• Una parte decimal: bcd ...
• Una potencia de base 10 con exponente entero: 10n
N x 10n
El número de átomos en 12 g de carbono:
602 200 000 000 000 000 000 000 6,022 x 1023
La masa de un átomo de carbono en gramos:
0,0000000000000000000000199 1,99 x 10-23
N es un número
entre 1 y 10
n es un número entero
positivo o negativo
En notación científica
40. Observa los números siguientes. ¿Cuál de los números está
escrito en notación científica?
Número
¿Notación
científica?
Explicación
1,85x10-2
1,083x101/2
0,82x1014
10x1014
Si
No
No
No
1 ≤1,85 < 10
½ no es un entero
0,82 no es ≥ 1
10 no es < 10
-2 es un número entero
41. Dado un número en notación científica, llamamos orden de magnitud al
exponente de la potencia de 10. Nos da una idea clara de cómo es el
número con el que estamos tratando. Por ejemplo, si es 6, estamos
hablando de millones; si es 12, de billones; si es –3, de milésimas, etc.
Orden de magnitud
tiene cinco dígitos enteros; tendremos que
desplazar la coma hacia la izquierda 4
lugares, es decir, 20 300 = 2,03 x 104.
tiene como primer dígito no nulo 5. Habrá
que desplazar la coma hacia la derecha 5
lugares; 0,000056 = 5,6 x 10-5.
20 300
0,000056
43. Expresar un número en notación científica
0,0 0 0 0 2 2 0 5 2,205 x 10–5
6 5 4 3 2 1
1 2 3 4 5
Nº en notación decimal Nº en notación científica
3190000,0
3 190 000 3,19 x 106
=
=
44. 123 × 10−8
1,23 × 10−6
12,3 × 10−7
Ejemplo: El número 0,00000123 puede escribirse en notación científica como:
Evitamos escribir los ceros decimales del número, lo que
facilita tanto la lectura como la escritura del mismo,
reduciendo la probabilidad de cometer erratas.
Observamos que existen múltiples posibilidades de expresar
el mismo número, todas ellas igualmente válidas.
45. ¿Cuál de los números está escrito en notación científica?
A) 4,25 x 100.08
B) 0,425 x 107
C) 42,5 x 105
D) 4,25 x 106
A) 4,25 x 100.08
Incorrecto. El exponente debe ser un entero y 0,08 no es un entero. La
respuesta correcta es 4,25 x 106.
B) 0,425 x 107
Incorrecto. Esto no es notación científica porque 0,425 es menor que 1. La
respuesta correcta es 4,25 x 106.
C) 42,5 x 105
Incorrecto. Esta no es notación científica porque 42,5 es mayor que 10. La
respuesta correcta es 4,25 x 106.
D) 4,25 x 106
Correcto. Esta es notación científica. 4,25 es mayor que uno y menor que 10,
y 6 es un entero.
46. Expresar un número dado en notación científica
en notación decimal
1,234 x 10–6
Puesto que el exponente es –6,
hacer el número más pequeño
moviendo la coma decimal 6
lugares a la izquierda. Si faltan
dígitos, se añade ceros.
000 001,234
3,04 x 105
Puesto que el exponente es 5,
hacer el número más grande
moviendo la coma decimal 5
lugares a la derecha. Si faltan
dígitos, se añade ceros.
3,04 000
0,000 001 234
Por tanto,
1,234 x 10–6 = 0,000 001 234
304 000
Por tanto,
3,04 x 105 = 304 000
47. Ahora comparemos algunos ejemplos de números expresados en notación científica y en notación
decimal estándar para entender cómo se convierte de uno al otro. Observa las tablas siguientes,
Pon atención al exponente en la notación científica y la posición del punto decimal en la notación
decimal.
Para escribir un número grande en
notación científica, movemos el punto
decimal a la izquierda hasta obtener un
número entre 1 y 10. Como mover el punto
decimal cambia el valor, es necesario
multiplicar el decimal por una potencia de
10 para que la expresión conserve su valor.
180 000 = 18000,0 x 101
= 1800,00 x 102
= 180,000 x 103
= 18,0000 x 104
= 1,80000 x 105
Veamos un ejemplo
Números Grandes
Notación Decimal Notación Científica
500,0 5 x 102
80 000,0 8 x 104
43 000 000,0 4,3 x 107
62 500 000 000,0 6,25 x 1010
Números Pequeños
Notación Decimal Notación Científica
0,05 5 x 10-2
0,0008 8 x 10-4
0,00000043 4,3 x 10-7
0,000000000625 6,25 x 10-10
48. La población mundial se estima en
alrededor de 6 800 000 000 personas.
¿Qué respuesta expresa este número en
notación científica?
A) 7 x 109
B) 0,68 x 1010
C) 6,8 x 109
D) 68 x 108
A) 7 x 109
Incorrecto. La notación científica reescribe los números, no los redondea. La respuesta
correcta es 6,8 x 109.
B) 0,68 x 1010
Incorrecto. Si bien 0,68 x 1010 es equivalente a 6 800 000 000; 0.68 no está en notación
científica ya que 0,68 no está entre 1 y 10. La respuesta correcta es 6,8 x 109.
C) 6,8 x 109
Correcto. El número 6,8 x 109 es equivalente a 6 800 000 000 y usa el formato apropiado
para cada factor.
D) 68 x 108
Incorrecto. Si bien 68 x 108 es equivalente a 6 800 000 000, no está escrito en notación
científica ya que 68 no está entre 1 y 10. La respuesta correcta es 6,8 x 109.
49.
50.
51. Operaciones con números en notación científica
Realizar cálculos con números escritos en notación científica es muy fácil:
basta con operar, por un lado, con los números que aparecen antes de la
potencia de 10 y, por otro, con las potencias.
Suma y resta en notación científica
Consideremos la suma 2,35 x 107 + 1,264 x 107. Como el exponente de
ambos números es el mismo, basta con sacar factor común 107:
2,35 x 107 + 1,264 x 107 = (2,35 + 1,264) x 107 = 3,614 x 107
Cuando el exponente de ambos es diferente, se reducen a exponente
común (el mayor de ellos) multiplicando el menor por la potencia de 10
adecuada.
52. 4,31 x 104 + 3,9 x 103 =
= 4,31 x 104 + 0,39 x 104 =
= (4,31 + 0,39)x104 = 4,70 x 104
Ejemplo:
Ejemplo: Calcula la suma
Escribimos los dos números con
el mismo exponente (el mayor).
3,9 x 103 = 0,39 x104
(1,2 x 103) + (3,4 x 105)
(0,012 x 105) + (3,4 x 105) =(0,012 + 3,4) x 105
= 3,412 x 105
Escribe 1,2 ·103 con exponente5.
Suma 2
1,2 x 103 = 0,012 x 103+2=5
Desplaza 2
53. Para realizar restas se sigue el mismo proceso: se reducen al exponente
mayor y se resta la parte entera o decimal de ambos números.
Ejemplo: (3,4 x 105) – (1,2 x 104)
(3,4 x 105) – (0,12 x 105) =
(3,4 – 0,12) x 105
= 3,28 x 105
Suma 1
1,2 x 104 = 0,12 x 104+1=5
Desplaza 1
= 1,52 x 10–6
= 5,5966 x 10–6
3,4 x 10–9 = 0,0034 x 10–9+3=–6
Desplaza 3
Ejemplo:
(1,2 x 10–6) + (3,2 x 10–7) = (1,2 x 10–6) + (0,32 x 10–6) = (1,2 + 0,32) x 10–6
Ejemplo:
(5,6 x 10–6) – (3,4 x 10–9) = (5,6 x 10–6) – (0,0034 x 10–6) = (5,6 – 0,0034)x10–6
3,2 x 10–7 = 0,32 x 10–7+1=–6
Desplaza 1 Suma 1
Suma 3
54.
55. Multiplicación y división en notación científica
Para multiplicar números en notación científica, multiplica los primeros
factores decimales y suma los exponentes.
Ejemplo: Multiplica (3,2 x 10–7) x (2,1 x 105)
(3,2 x 2,1) x 10–7+5 = 6,72 x 10-2
Ejercicio: Multiplica (9 x 107) x (1,5 x 104)
Para dividir números en notación científica, divide el primer factor decimal del
numerador por el primer factor decimal del denominador. Entonces resta el
exponente del denominador al exponente del numerador.
Ejercicio: Divide (2,4 x 10–7) (3,1 x 1014)
Ejemplo: Divide (6,4 x 106) (1,7 x 102)
(6,4 1,7) x 106–2 = 3,76 x 104
7,74 x 10-22
1,35 x 1012
62. TEMPERATURA
La temperatura de un cuerpo se define
como una magnitud que define la
energía media de las moléculas que
constituye ese cuerpo
63. ¿Quién la inventó?
ANDERS CELSIUS
¿Puntos de referencia?
Puntos de congelación y ebullición
del agua
Datos.
Temperaturas Negativas.
-273°C Cero Absoluto
64. ¿Quién la inventó?
LORD KELVIN
¿Puntos de referencia?
Punto de inicio (el cero absoluto)
Datos.
No hay temperaturas negativas.
El tamaño de los grados con
respecto a la escala CELSIUS son
iguales.
65. ¿Quién la inventó?
GABRIEL FAHRENHEIT
¿Puntos de referencia?
Puntos de congelación y ebullición
del agua
Datos.
P.C. = 32° y P.E.= 212°
La diferencia entre los puntos de
referencia es de 180 grados o partes
66. ¿Quién la inventó?
WILLIAM RANKINE
¿Puntos de referencia?
Punto de inicio, el cero absoluto de la
escala FAHRENHEIT.
Datos.
P.C. = 492° y P.E.= 672°
No hay temperaturas negativas Intervalos
idénticos a la escala Fahrenheit.
75. PARA PRACTICAR EN CASA …
Convertir 500 mm/s a Km/min
Convertir 1200 m3/cs a cL/h
Convertir 0,0055 x105 g/mL a Kg/m3
Convertir 5x103 g/cL a Mg/nL
Convertir 0,0256 x104 °C a R
Convertir 15000 x10-3 °F a °C
Convertir 12,3 x104 dg/s a lb/día
Convertir 0,540 x104 °F a R
Convertir 25 m3/min a mL/ms
Convertir 5x103 pg/dL a hg/L
78. Las cifras significativas (o dígitos significativos) representan el uso de una
escala de incertidumbre en determinadas aproximaciones.
El uso de éstas considera que el último dígito de aproximaciones incierto,
por ejemplo, al determinar el volumen de un líquido con una probeta
cuya precisión es de 1 ml, implica una escala de incertidumbre de 0,5 ml.
Así se puede decir que el volumen de 80ml será realmente de 79,5 ml a
80,5 ml. El volumen anterior se representará entonces como (80,0 ±
0,5)ml.
82. CIFRAS SIGNIFICATIVAS
0, 00005400
Todos los números
distintos de cero
son significativos
Los ceros no son
significativos después
de un decimal antes
de números distintos
de cero
Los ceros después de números
distintos de cero en un decimal
son significativos
83. Ejemplo:
14,55 Los dígitos distintos
de cero siempre son
significativos
4 cifras
0,20 2 cifras
0,003010 4 cifras
Todo cero al final y a la
derecha de la primera
cifra significativa, es
significativo
84. Ejemplo:
101 Los ceros entre dos
números son también
significativos
3 cifras
0,0000001 1 cifra
0,03 1 cifra
Los ceros utilizados
para localizar la coma
decimal NO son
significativos
2,404 4 cifras
Los ceros a la izquierda del primer dígito que no es cero sirven
solamente para fijar la posición del punto decimal y no son significativos
85. Ejemplo:
0,0320 3 cifras
4700 2 cifras
4700,0 5 cifras
32,00 4 cifras
En un número con dígitos
decimales, los ceros finales
a la derecha del punto
decimal son significativos
Si un número no tiene punto decimal y termina
con uno o más ceros dichos ceros pueden ser o no
significativos. Para poder especificar el número de
C. S. se requiere información adicional y se expresa
el número en notación científica, pero si se indica
el punto decimal, entonces los cero son
significativos.
86. RESUMIENDO …
1. Cualquier dígito diferente de cero es
significativo.
2. Ceros al final después del punto decimal a la
derecha son significativos.
3. Ceros entre dígitos distintos de cero son
significativos.
4. Ceros usados para establecer valor posicional
no son significativos. Ceros a la izquierda del
primer dígito distintos de cero no son
significativos. Los ceros al final de un número
entero pueden ser o no significativos.
5. Si un número es mayor que uno, todos los ceros
a la derecha del punto decimal son significativos.
6. Si el número es menor que uno, entonces
únicamente los ceros que están al final del
número y entre los dígitos distintos de cero son
significativos
87. CIFRAS SIGNIFICATIVAS
“Todos los dígitos de un número, menos los ceros a la izquierda”
13 13,0 0,213 0,20 0,205
0,004782 12,726 128314
2 c. s. 3 c. s. 3 c. s. 2 c. s. 3 c. s.
4 c. s. 5 c. s. 6 c. s.
En química expresamos los resultados con 3 cifras significativas
…CRITERIOS DE REDONDEO…
88. CRITERIOS DE REDONDEO
Si el valor del primer dígito que se descarta es …
Al último dígito que se
conserva se le suma 1
El último dígito que se
conserva queda igual
Ejemplos
0,2 0 5 7 Expresado con 3 c.s.
Último que
se conserva
Primero que
se descarta
0,206
…mayor o igual que 5 …menor que 5
1 2,7 2 6 Expresado con 3 c.s. 12,7
128514 Expresado con 3 c.s. …?
89. NOTACION CIENTIFICA
Modo conveniente de expresar números, especialmente para los
muy grandes o muy pequeños
Se escribe sólo un dígito distinto de cero en la parte entera, y se
acompaña de una potencia de base 10
Ejemplos:
1,28514 x 10 5
5 lugares
Expresado en notación científica
Con 3 cifras significativas 1,29 x 10 5
Expresado en notación científica
Con 3 cifras significativas
0,004782 4,782 x 10 -3
3 lugares
4,78 x 10 -3
90. MARGEN DE ERROR
En química, salvo indicación contraria, se admite un 3 % de error
… Cómo saber si mi respuesta será válida o no?
Respuesta de la guía
+ su 3 %
- su 3 %
206 g
194 g
“Todos los valores
entre 194 y 206
serán tomados
como válidos”
200 g
Respuesta correcta del
parcial 0,0110 g
+ su 3 %
- su 3 %
0,0113 g
0,0107 g
“Interalo de
resultados
válidos”
…Un alumno respondió 0,01 g …Es válida?
91. PARA PRACTICAR …
Determinar el número de cifras significativas en las siguientes cantidades:
2804 m
-2,84 Km
0,0029 mL
0,003068 g
8,1x104 s
12345 m
70x10-5 h
1999,0 cm
20200 mm
4 cifras
3 cifras
2 cifras
4 cifras
2 cifras
5 cifras
1 cifra
5 cifras
3 cifras