Significant digits
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The document discusses the rules for determining significant digits in measurements and calculations. It defines 5 rules for identifying significant digits in a number. It then provides 3 rules for performing calculations while maintaining the appropriate number of significant digits: when multiplying and dividing use the least number of significant digits, when adding and subtracting use the least number of decimal places, and round numbers according to whether the preceding digit is odd or even. Several examples of calculations involving significant digits are provided.
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Significant Figures
This document discusses significant figures and measurement uncertainty. It provides examples of exact vs measured numbers, rules for determining significant figures, and how to properly round measurements. Key points include:
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Significant figures 1
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Significant Figures
This document provides information about significant figures and how they are used in scientific measurements and calculations. It defines significant figures as the reliable digits in a measurement that are known with certainty, indicating the accuracy of the measurement. Rules are presented for determining the number of significant figures in given measurements, as well as rules for performing calculations while preserving the correct number of significant figures based on the least accurate measurement in the calculation. Examples are provided to demonstrate applying the significant figures rules when adding, subtracting, multiplying and dividing measurements.
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This document discusses significant figures and measurement uncertainty. It provides examples of exact vs measured numbers, rules for determining significant figures, and how to properly round measurements. Key points include:
- Measured numbers have uncertainty since the last digit is an estimate
- There are 4 rules for determining if a zero is significant
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This document discusses the rules for determining significant digits in measurements and calculations. It defines four main rules:
1. All non-zero digits are significant, as are zeros between non-zero digits.
2. Leading zeros are not significant.
3. Trailing zeros may or may not be significant, depending on whether a decimal is present.
4. In calculations, the answer should match the least number of significant digits in the input values.
It provides examples like 0.08006 having 4 significant digits, and 1000mL having 1 significant digit. The document also covers rounding rules and calculating volumes and perimeters based on measurements to the correct number of significant digits.
Sig Figs
1. Significant figures indicate the precision or uncertainty of a measurement. Exact numbers are obtained by counting or definition while measured numbers use measuring devices and have uncertainty.
2. There are rules for determining which digits in a measured number are significant based on their position relative to the decimal point. Numbers should be rounded appropriately based on the number of significant figures.
3. Calculations with measured numbers must follow rules to avoid reporting more significant figures than the original measurements support, such as limiting digits in addition/subtraction and figures in multiplication/division.
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Define the significant figures
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Calculate the whole number and determine the significant figures.
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- Prefixes are used to indicate the power of 10 being multiplied, with examples including mega (106) and micro (10-6).
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Chapter02 Measurements (Significant Figures) Lec-07
Learning Objectives
Review
Introduction to significant figures
Rules of Significant figures
Practice Questions
Review Questions
Significant Figures
Only those figures or digits of a numerical quantity which are the result of actual measurement are said to be significant.
Rules of Significant Figures
Rule 01 All non zeros are significant figures Example. 3.14
Rule 2 Zeros Between non zeros are significant Example 1001
Home Task
Write the number of significant figures
(1, 400, 12002,100.0, 0.0001,10x104, 150.000, 17000,1200.010, 1222.00, 111, 000, 1.000)
Thank You For Your Cooperation
Presentation On SlideShare “Significant Figures (Measurments) Lec 07”
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Significant figures are used to indicate the precision of a measurement or calculation. There are three types of zeros in numbers: leading zeros do not count as significant figures, captive zeros between nonzero digits do count, and trailing zeros count only if a decimal is present. When adding or subtracting measurements, the answer can have no more decimal places than the least precise measurement. When multiplying or dividing measurements, the result can have no more significant figures than the least reliable measurement.
Significant figures
This document discusses significant figures and how they are used in science. It defines significant figures as the digits in a measurement that are known with certainty. Measurements are approximate numbers, while amounts of money are exact numbers. When recording measurements, only digits that are dependable based on the precision of the measuring tool are written down. The number of significant figures is determined by counting all digits starting from the first non-zero digit, with some exceptions for trailing zeros. Calculations with measurements require rules for rounding based on the least precise term to determine the number of significant figures in the final answer.
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 × 10n, where 1 ≤ M < 10 and n is an integer exponent.
LESSON-7_Uncertainties-in-Measurement.pptx
This document discusses measurement uncertainty and significant figures. It explains that all measurements have some degree of uncertainty due to imprecise measuring devices. It provides examples of measuring the volume of a liquid and how three students could report different values due to this uncertainty. The document then defines the rules for determining the number of significant figures in a measurement, including that trailing zeros are significant but leading zeros are not. It explains how to handle calculations, noting that results should be rounded or truncated to the least number of significant figures of the original measurements. Finally, it defines accuracy as how close a measurement is to the true value, and precision as how close repeated measurements are to each other.
Significant Digits
Significant digits are used to represent the level of uncertanty while reporting numbers collected through a measurement device
Mathematical Skills I - Rounding Numbers
The document discusses rules for rounding numbers to a specified number of decimal places. It explains that rounding means making a number simpler while keeping its value close to the original. It then outlines four cases for rounding numbers based on the value of the digit being dropped: 1) if greater than 5, round up, 2) if less than 5, leave the same, 3) if exactly 5 with no following digits, round up if odd and leave the same if even, 4) if exactly 5 with following nonzero digits, round up. Examples are provided to illustrate each case.
PowerPointCh2_Section2.3.pdf
This document discusses significant figures, uncertainty in measurement, accuracy, and precision. It provides examples and rules for counting significant figures, including that non-zero digits, captive zeros, and sometimes trailing zeros are significant. Leading zeros are never significant. Measurements should be reported with the correct number of significant figures and including the uncertainty, which is usually the last digit. Uncertainty comes from the limitations of measurement tools and is calculated from the increment, which is the smallest unit of measurement. Accuracy refers to how close a measurement is to the true value, while precision refers to the agreement between multiple measurements of the same quantity.
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Significant digits
- 2. SIGNIFICANT DIGITS Rule #1: All non-zero numbers are significant Ex. 5489.213 7 significant digits
- 3. SIGNIFICANT DIGITS Rule #2: All zeros located between non-zero numbers are significant Ex. 0.08006 4 significant digits
- 4. SIGNIFICANT DIGITS Rule #3: Zeros located to the left of a value are not significant Ex. 0.00004 1 significant digit
- 5. SIGNIFICANT DIGITS Rule #4: Zeros that are located to the right of a value may or may not be significant Ex. 1000.mL 4 significant digits Ex. 1000mL 1 significant digit
- 6. SIGNIFICANT DIGITS Ex. 1000mL 1 significant digit Why? 1000mL could have been anything from 951mL to 1049mL
- 7. SIGNIFICANT DIGITS Ex. 1000.0mL 5 significant digits Why? Rule #5 Any 0’s to the right of a decimal that are not followed by any number are significant
- 8. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #1: Multiplying and Dividing 1.008 x 4.67 = 4.70736 = 4.71 This value has the lowest number of significant digits The value with the lowest number of significant digits determines how many significant digits will appear in the answer
- 9. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #2: Adding and Subtracting 1.008 + 4.67 = 5.678 = 5.68 This value has the lowest number of decimal places The value with the lowest number of decimal places determines how many decimal places will appear in the answer
- 10. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If greater than 5, round up If less than 5, round down
- 11. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round up if the preceding number is odd Ex. 18.35 Odd number 18.4
- 12. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round down if the preceding number is even Ex. 18.25 Even number 18.2
- 13. CALCULATIONS WITH SIGNIFICANT DIGITS 12cm 6.782cm 5.18cm Calculate the volume of the rectangular prism
- 14. CALCULATIONS WITH SIGNIFICANT DIGITS V= l x w x h = (5.18cm) x (6.782cm) x (12cm) = 421.56912cm 3 = 4.2 x 10 2 cm 3 “ 12” has the lowest number of significant digits. So the answer must have 2 significant digits. 12cm 6.782cm 5.18cm
- 16. SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm
- 18. SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm = 12.0373cm = 12cm = 1060.20288cm 3 = 1.1x10 3 cm 3