Mathematical skills III - Scientific Noation
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This document provides an overview of scientific notation. It explains that scientific notation is used to represent large or small numbers in a condensed form by writing them as the product of a number between 1 and 10 and a power of 10. The document provides examples of converting numbers to and from scientific notation. It also demonstrates how to perform multiplication and division in scientific notation by adding or subtracting the exponents. Finally, it includes practice problems for the reader.
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The document discusses scientific notation, which is a way to write very large or small numbers in a more compact form using two factors - a number between 1 and 10 multiplied by a power of 10. It provides examples of converting numbers between standard form and scientific notation, such as 2.3 x 103 representing 2300. The Andromeda Galaxy contains at least 200 billion stars, which can be written more concisely in scientific notation as 2 x 1011 stars.
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The document discusses scientific notation and operations involving numbers written in scientific notation. It explains that for addition or subtraction, the exponents must be the same. If exponents are different, the decimal must be moved in one number so that the exponents match before performing the operation. Examples are provided for adding and subtracting numbers with the same and different exponents, demonstrating the steps to obtain the final answer in proper scientific notation form.
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This document provides instruction on scientific notation and powers of 10. It begins with examples of evaluating and multiplying numbers by powers of 10 by moving the decimal point left or right. It then discusses writing numbers in terms of powers of 10 based on the number of places the decimal point is from 1. The document also covers converting between standard notation and scientific notation. It applies these concepts to astronomy examples of writing planet diameters and distances in standard and scientific notation. Finally, it discusses comparing and ordering numbers expressed in scientific notation.
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This document provides information on scientific notation and how to perform calculations using numbers expressed in scientific notation. It defines scientific notation as expressing numbers in the form of N x 10x, where N is the coefficient and x is the exponent. It explains how to convert between standard and scientific notation by moving the decimal point based on the exponent. When performing calculations, it describes adding or subtracting exponents for multiplication and division, and converting both numbers to the same exponent for addition and subtraction.
Scientificnotation
Scientific notation is a way to write very large or small numbers in a more compact form. To write a number in scientific notation, you express it as the product of two factors: a decimal number greater than or equal to 1 but less than 10, and a power of 10. For example, 93,000,000 would be written as 9.3 x 107. The power of 10 indicates how many places the decimal is moved. Very small decimals between 0 and 1 use a negative power of 10. For example, 0.00064 would be written as 6.4 x 10-4. Scientific notation makes large and small numbers easier to work with
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This document provides information on scientific notation and how to perform calculations using numbers expressed in scientific notation. It defines scientific notation as expressing numbers in the form of N x 10x, where N is the coefficient and x is the exponent. It explains how to convert between standard and scientific notation by moving the decimal point based on the exponent. When performing calculations, it describes adding or subtracting exponents for multiplication and division, and converting both numbers to the same exponent for addition and subtraction.
Scientificnotation
Scientific notation is a way to write very large or small numbers in a more compact form. To write a number in scientific notation, you express it as the product of two factors: a decimal number greater than or equal to 1 but less than 10, and a power of 10. For example, 93,000,000 would be written as 9.3 x 107. The power of 10 indicates how many places the decimal is moved. Very small decimals between 0 and 1 use a negative power of 10. For example, 0.00064 would be written as 6.4 x 10-4. Scientific notation makes large and small numbers easier to work with
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Scientific notation
Scientific notation is a method used to write very large or small numbers in a standardized form. It expresses numbers as the product of a number between 1 and 10 and a power of 10. This allows easier calculations with numbers that would otherwise be difficult to work with in standard form due to the number of zeros. Some key points covered are:
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- When adding or subtracting terms with the same exponent, we simply add or subtract the leading numbers and keep the exponent.
- For terms with different exponents, we move the decimal in the number with the smaller exponent to equalize the exponents
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1) Scientific notation is used to express very large or small numbers in a more compact form. It expresses numbers as the product of a number between 1 and 10 and a power of 10.
2) To convert a number to scientific notation, the decimal is moved to place the number between 1 and 10, and the power of 10 is determined by the number of places moved. Positive exponents indicate moving left, negative right.
3) When adding or subtracting numbers in scientific notation, they must first be converted to the same power of 10 before performing the operation. Multiplication and division directly apply the rules of adding or subtracting exponents.
Scientific Notation
This document provides information on scientific notation and how to perform calculations using numbers expressed in scientific notation. It defines scientific notation as expressing numbers in the form of N x 10x, where N is the coefficient and x is the exponent. It explains how to convert between standard and scientific notation by moving the decimal point and counting places. The document also outlines how to perform addition, subtraction, multiplication and division when numbers are in scientific notation by manipulating the coefficients and exponents.
Scientific Notation
Scientific notation is used in science to conveniently write very large or small numbers. It is easier to work with numbers in scientific notation mathematically, such as when multiplying, dividing, or taking powers, by simply adding or subtracting the exponents rather than writing out long strings of zeros. Scientific notation therefore makes performing calculations simpler.
Number system conversion
This document introduces group members Md. Ilias Bappi and Md.Kawsar Hamid and presents information on number systems and conversions. It discusses the decimal number system and defines ones' complement and twos' complement in binary. It provides examples of converting between binary, decimal, octal, and hexadecimal systems using appropriate techniques like multiplying bit positions by powers of the base. Conversions include binary to decimal, octal to decimal, hexadecimal to decimal, decimal to binary, octal to binary, hexadecimal to binary, decimal to octal, octal to hexadecimal, and binary to decimal representations of fractions.
1-4 Scientific Notation
1. Scientific notation is used to express very large or very small numbers in a standard way using a coefficient and power of 10.
2. Theories are explanations based on repeated experimentation and observation, while laws are rules of nature. Theories do not become laws.
3. Significant figures tell us how precisely a measurement or number is known and indicate the reliability of the last digits.
4 2scientific notation
The document discusses scientific notation and powers of 10. It explains that in scientific notation, any number x can be written as the product of a number r and a power of 10, r ร 10N, where 1 โค r < 10 and N is an integer. A positive exponent N shifts the decimal point of r to the right, while a negative N shifts it left. Converting between standard and scientific notation simply moves the decimal in r by the number of places indicated by N.
1-3 Scientific Notation
1. Scientific notation is a way to write numbers as a product of a coefficient and a power of 10 to express very large and very small numbers.
2. A law is a statement of fact based on repeated observation that describes natural phenomena, while a theory is a well-substantiated explanation of such a law.
3. Significant figures indicate the precision or uncertainty of a measurement and are used to calculate the error in products and quotients of calculations.
Scientific notation
This document contains notes from a math class covering scientific notation. It includes examples of converting numbers between standard and scientific notation by moving the decimal point left or right based on positive and negative exponents. Students are provided steps to write numbers in scientific notation involving identifying the exponent and decimal direction. The class covers vocabulary of scientific notation and worked through examples of conversion between the two forms. Homework on exponents was assigned.
Number systems
This document discusses different number systems including decimal, binary, octal, and hexadecimal. It provides details on how to convert between these number systems including techniques for converting between their digit representations. Examples are given for converting values between decimal, binary, octal, and hexadecimal number bases. Common number prefixes and powers are also defined.
Scientific notation (day 2)
This document provides a lesson on scientific notation. It begins with examples of writing numbers like populations in scientific notation. It then gives examples of adding and subtracting numbers in scientific notation, showing how to equalize exponents. The document explains that scientific notation allows precise approximation of very large and small numbers by showing order of magnitude. It concludes that scientific notation facilitates tracking and comparing extremely large or small values.
Measurements And Calculations
1. The scientific method involves making observations and measurements, formulating hypotheses to explain observations, and performing experiments to test hypotheses.
2. Scientific theories are sets of hypotheses that have been tested and provide explanations for natural phenomena, while scientific laws summarize repeated experimental observations of natural phenomena.
3. Scientific notation is used to conveniently express very large and small numbers and involves writing numbers in the form of M ร 10n, where 1 โค M < 10 and n is an integer exponent.
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1. b
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
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Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
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1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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- 2. Scientific notation is a short way of representing such numbers without writing the place-holding zeros. SCIENTIFIC NOTATION Population of the world is around 7,500,000,000 people Mass of a dust particle is 0.000000000753 kg Approximate speed of light is 1,080,000,000 km/h 0.00000000000000000000000000000091093822 kg Distance from the sun to the nearest star is 39,900,000,000,000 km Mass of an electron is
- 3. ๏ท Step 1: Identify the number without the place-holding zeros. โ 653 ๏ท Step 2: Place the decimal point after the leftmost digit. โ 6.53 ๏ท Step 3: Find the exponent by counting the number of places that you moved the decimal point The decimal point was moved 8 places to the left. Therefore, the exponent of 10 is positive 8. Remember, if the decimal point had moved to the right, the exponent would be negative. ๏ท Step 4: Write the number in scientific notation. โ 6.53 x 108 Scientific notation is a short way of representing such numbers without writing the place-holding zeros. SCIENTIFIC NOTATION In scientific notation, we write the number as a product of two factors: the first is a number -m- between 1 and 10, and the second is a power of ten raised to the -n- power, written as 10exponent. m x 10n Sample Problem: Write 653,000,000 in scientific notation
- 4. Scientific notation is a short way of representing such numbers without writing the place-holding zeros. SCIENTIFIC NOTATION In scientific notation, we write the number as a product of two factors: the first is a number -m- between 1 and 10, and the second is a power of ten raised to the -n- power, written as 10exponent. m x 10n Original number Number in scientific notation Population of the world is around 7,500,000,000 people Approximate speed of light is 1,080,000,000 km/h Mass of a dust particle is 0.000000000753 kg Distance from the sun to the nearest star 39,900,000,000,000 Mass of an electron 0.000000000000000000000000 00000091093822 kg
- 5. ๏ท Step 1: Multiply the decimal numbers. โ 2.6 x 6.3 = 16.38 ๏ท Step 2: Add the exponents. โ 7 + 4 = 11 ๏ท Step 3: Put the new decimal number with the new exponent in scientific notation form. โ 16.38 x 1011 ๏ท Step 4: Because the new decimal number is greater than 10, count the number of places the decimal moves to put the number between 1 and 10. Add this number to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent. โ 1 6.38 x 1011 โ 1.638 x 1012 Scientific notation is a short way of representing such numbers without writing the place-holding zeros. SCIENTIFIC NOTATION Multiply in Scientific Notation Multiply their coefficients and add their exponents.r a x 10n ยท b x 10m = (a ยท b) x 10 (n + m) Sample Problem: Multiply (2.6 x 107) by (6.3 x 104).
- 6. ๏ท โข Step 1: Divide the decimal numbers. โ 1.23 รท 2 .4 = 0.5125 ๏ท โข Step2: Subtract the exponents of the powers of 10. โ 11 - 4 = 7 ๏ท โข Step 3: Place the new power of 10 with the new decimal in scientific notation form. โ 0.5125 x 107 ๏ท โข Step 4: Because the decimal number is not between 1 and 10, move the decimal point one place to the right and decrease the exponent by 1. โ 0.5 125 x 107 โ 5.125 x 106 Scientific notation is a short way of representing such numbers without writing the place-holding zeros. SCIENTIFIC NOTATION Divide in Scientific Notation Multiply their coefficients and add their exponents.r a x 10n b x 10m = a b x 10 (n - m) Sample Problem: Divide (1.23 x 1011) by (2.4 x 104)
- 7. PRACTICE! a x 10n b x 10m = a b x 10 (n โ m)) Problem New decimal New exponent Answer (5.76 x 109) x (3.2 x 103) (3.72 x 108) x (1.2 x 105) (6.4 x 10-4) รท (4 x 106) (3.7 x 104) รท (5.2 x 105) a x 10n ยท b x 10m = (a ยท b) x 10 (n + m)