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Chapter 1 Measurements

1.4Significant Figures in

Calculations

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Rounding Off Calculated Answers

In calculations,

• answers must have the same number of significant figures as the measured numbers.

• a calculator answer often must be rounded off.

• rounding rules are used to obtain the correct number of significant figures.

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Rounding Off Calculated Answers

When the first digit dropped is 4 or less,

• the retained numbers remain the same.

45.832 rounded to 3 significant figures

drops the digits 32 = 45.8

When the first digit dropped is 5 or greater,

• the last retained digit is increased by 1.

2.4884 rounded to 2 significant figures

drops the digits 884 = 2.5 (increase by 0.1)

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Adding Significant Zeros

• Sometimes a calculated answer requires more significant digits. Then, one or more zeros are added.

Calculated Zeros Added to Answer Give 3 Significant Figures

4 4.001.5 1.500.2 0.200

12 12.0

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Learning Check

Round off or add zeros to the following calculated answers to give three significant figures.

A. 824.75 cm

B. 0.112486 g

C. 8.2 L

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Solution

Adjust the following calculated answers to give answers

with 3 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 is added.

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Calculations with Measured Numbers

In calculations with measured numbers, significant figures ordecimal places arecounted to determinethe number of figures inthe final answer.

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When multiplying or dividing

• the final answer must have the same number of significant figures as the measurement with the fewest significant figures.

• use rounding rules to obtain the correct number of significant figures.

Example:

110.5 x 0.048 = 5.304 = 5.3 (rounded)

4 SF 2 SF calculator 2 SF

Multiplication and Division

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Select the answer 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

Learning Check

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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)

Solution

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When adding or subtracting

• the final answer must have the same number of decimal places as the measurement with the fewest decimal places.

• use rounding rules to adjust the number of digits in the answer.

25.2 one decimal place

+ 1.34 two decimal places

26.54 calculated answer

26.5 final answer with one decimal place

Addition and Subtraction

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For each calculation, round off the calculated answer to give a final answer with the correct number of significant figures.

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

Learning Check

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A. 235.05 +19.6 + 2 256.65 round to 257 Answer (1)

B. 58.925 -18.2

40.725 round to 40.7 Answer (3)

Solution