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# 2 4 significant_fig_in_calc

## by Paul Cuaresma, Working at The Street and Jungles of Guam on Sep 19, 2011

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## 2 4 significant_fig_in_calcPresentation Transcript

• Chapter 2 Measurements
• 2.4
• Significant Figures in
• Calculations
• In calculations
• answers must have the same number of significant figures as the measured numbers
• calculated answers are usually rounded off
• rounding rules are used to obtain the correct number of significant figures
• When the first digit dropped is 4 or less , the retained numbers remain the same.
• to round off 45.832 to 3 significant figures
• drop the digits 32 = 45.8
• When the first digit dropped is 5 or greater , the last retained digit is increased by 1.
• to round off 2.4884 to 2 significant figures
• drop the digits 884 = 2.5 ( increase by 0.1)
• Sometimes a calculated answer requires more significant digits. Then one or more zeros are added .
• Answer Give 3 Significant Figures
• 4 4.00
• 1.5 1.50
• 0.2 0.200
• 12 12.0
• Learning Check
• answers with three significant figures:
• A. 824.75 cm
• B. 0.112486 g
• C. 8.2 L
• Solution
• answers with three significant figures:
• A. 825 cm first digit dropped is greater than 5
• B. 0.112g first digit dropped is 4
• C. 8.20 L significant zero added
• Calculations with Measured Numbers
• In calculations with measured numbers, significant figures or decimal places are used to determine the correct number of figures in the final answer.
• When multiplying or dividing , use
• the same number of significant figures (SFs) as in the measurement with the fewest significant figures
• rounding rules to obtain the correct number of significant figures
• Example
• 110.5 x 0.048 = 5.304 = 5.3 (rounded)
• 4 SFs 2 SFs calculator 2 SFs
• Give an answer for each with the correct
• number of significant figures.
• A. 2.19 x 4.2 =
• 1) 9 2) 9.2 3) 9.198
• B. 4.311 ÷ 0.07 =
• 1) 61.59 2) 62 3) 60
• C. 2.54 x 0.0028 =
• 0.0105 x 0.060
• 1) 11.3 2) 11 3) 0.041
• A. 2.19 x 4.2 = 2) 9.2
• B. 4.311 ÷ 0.07 = 3) 60
• C. 2.54 x 0.0028 = 2) 11
• 0.0105 x 0.060
• On a calculator, enter each number followed by
• the operation key.
• 2.54 x 0.0028  0.0105  0.060 = 11.28888889
• = 11 ( rounded off )
• When adding or subtracting , use
• the same number of decimal places as the measurement with the fewest decimal places
• rounding rules to adjust the number of digits in the answer
• 25.2 one decimal place
• + 1.34 two decimal places
• 26.5 final answer (one decimal place)
• For each calculation, round the answer to give
• the correct number of digits.
• A. 235.05 + 19.6 + 2 =
• 1) 257 2) 256.7 3) 256.65
• B. 58.925 - 18.2 =
• 1) 40.725 2) 40.73 3) 40.7