1

Chapter 2 Measurements

2.4Significant Figures in

Calculations

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

2

Rounding Off Answers

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

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

3

Rounding Off Calculated Answers

• 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)

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

4

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 4.00 1.5 1.50 0.2 0.200

12 12.0

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

5

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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6

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 added

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

7

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.

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

8

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

Multiplication and Division

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

9

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

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

10

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 off)

Solution

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

11

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

26.54 calculated answer

26.5 final answer (one decimal place)

Addition and Subtraction

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

12

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

Basic Chemistry Copyright © 2011 Pearson Education, Inc.

13

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

Basic Chemistry Copyright © 2011 Pearson Education, Inc.