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Chapter 2 Measurements

2.4Significant Figures in

Calculations

Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings

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Rounding Off Answers

Often, the correct answer

• Requires that a calculated answer be rounded off.

• Uses rounding rules to obtain the correct answer with the proper number of significant figures.

Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings

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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

• Occasionally, 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

Adjust the following calculated answers to give

answers with 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 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 is added.

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Calculations with Measured Numbers

In calculations with

measured numbers, • Significant figures are

counted or • Place values are

determined to give• The correct number of

figures in the final answer.

Copyright © 2008 by Pearson Education, Inc.Publishing as Benjamin Cummings

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When multiplying or dividing

• The answer has the same number of significant figures as in the measurement with the fewest significant figures.

• Rounding rules are used 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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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

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 bythe operation key.

2.54 x 0.0028 0.0105 0.060 = 11.28888889= 11 (rounded)

Solution

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When adding or subtracting use

• The same number of digits as the measurement whose last digit has the highest place value.

• 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 answer with one decimal place

Addition and Subtraction

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For each calculation, round the answer to givethe 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

Learning Check

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A. 235.05 hundredths place (2 decimal places)

+19.6 tenths place (1 decimal place) + 2 ones place 256.65 rounds to 257 Answer (1)

B. 58.925 thousandths place (3 decimal places) -18.2 tenths place (1 decimal place)

40.725 round to 40.7 Answer (3)

Solution