Chapter 2 Lecture

Basic ChemistryFourth Edition

Chapter 2 Measurements2.4 Significant Figures in Calculations

Learning Goal Adjust calculated answers to give the correct number of significant figures.

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In calculations

•calculated answers are usually rounded off

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

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Rounding Off

1. If the first digit to be dropped is 4 or less, then it and all following digits are simply dropped from the number.

2. If the first digit to be dropped is 5 or greater, then the last retained digit is increased by 1.

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Rules for Rounding Off

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Rounding Off and Significant Figures

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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Learning Check

Adjust the following calculated answers to give answers with three significant figures:

A. 824.75 cm 825 cm

B. 0.112486 g 0.112 g

C.8.2 L 8.20 L

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Solution

In multiplication and division, the final answer is written to have the same number of significant figures (SFs) as the measurement with the fewest SFs.

For example,

24.65 × 0.67 = 16.5155 17 4 SF 2 SF Calculator Final answer

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Multiplication and Division with Measured Numbers

When the calculator answer is a small whole number and more significant figures are needed, we can add one or more zeros.

For example,

= 4 4.00

3 SF Calculator Final answer

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Adding Significant Zeros

In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places.

For example, 2.367 Thousandths place

+ 34.1 Tenths place 36.467 Calculator display 36.5 Answer, rounded off to tenths place

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Addition and Subtraction with Measured Numbers

Give an answer for each with the correct number of significant figures.

A.2.19 × 4.2 = (1) 9 (2) 9.2 (3) 9.198

B. 2.54 × 0.0028 = 0.0105 × 0.060

(1) 11.3 (2) 11 (3) 0.041

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Learning Check

Give an answer for each with the correct number of significant figures.

A. 2.19 × 4.2 = (2) 9.2

B. 2.54 × 0.0028 = (2) 11 0.0105 × 0.060

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Solution

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

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Learning Check

A. 235.05 Hundredths place

+19.6 Tenths place

+ 2 Ones place

256.65 rounds to 257 answer (1)

B. 58.925 Thousandths place

–18.2 Tenths place

40.725 rounds to 40.7 answer (3)

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Solution