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Significant Figures

Significant Figures - Significant Figures Review Procedure...

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Significant Figures Review Procedure Different rules are needed for addition (and its reverse, subtraction) and multiplication (and its reverse, division). Both procedures require us to round off the answers to the correct number of significant figures. Rounding off In calculations, round up if the last digit is above 5 and round down if it is below 5. For numbers ending in 5, round up. For example, 2.35 rounds to 2.4. The quantity 14.348 cm 3 rounds to 14.3 cm 3 if the answer should have 3 sf, but it would have rounded to 14.35 cm 3 if the data had justified 4 sf. Rounding must be carried out in a single step: 14.348 cm 3 should not first be rounded to 14.35 cm 3 and then to 14.4 cm 3 . The correct procedure is to round off only at the final stage of the calculation and to carry all digits in the memory of the calculator until that stage. Addition and subtraction When adding or subtracting, the number of decimal places in the result should be the same as the smallest number of decimal places in the data. Multiplication and division When multiplying or dividing, the number of significant figures in the result should be the same as the smallest number of significant figures in the data. Integers and exact numbers When multiplying or dividing by an integer or an exact number, the uncertainty of the result is determined by the measured value. EXAMPLE Using significant figures when adding and subtracting Find the total volume of three blocks of copper with measured volumes 11.12,1.2, and 3.107 cm 3 . STRATEGY We need to add the volumes, so we should follow the rule for addition. SOLUTION The smallest number of digits after the decimal point is 1, in 1.2 cm 3 . Thus, only one digit should follow the decimal point in the total volume: Round to 15.4 cm 3 SELF-TEST 2.6A
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