UNIT # 1 Introduction Objectives Reading 1.1 Metric System 1.2 1.3 Scientific Notation 1.4 Dimensional Analysis 1.5 1.6 1.7 1.8 Problems 1 | 2 | 3

MEASUREMENT

1.7 - Calculations Involving Significant Figures

1.7.3 - Rules for Multiplication and Division

The answer must contain the same number of significant figures as were present in the measurement with the fewest number of significant figures.

Question: A student measures the length of a table to be 120.2 cm and the width to be 29.5 cm. What is the area of the table. Express the answer with the proper number of significant figures.

Step 1: To obtain the area of the table, we perform the following multiplication using the calculator.

29.5 cm x 120.2 cm = ?

The calculator displays the answer to be 3545.9. The unit is in cm2.

Step 2: Inspect each number and determine the number of significant figures in each number.

 29.5 3 significant figures (This measurement has the fewest number of significant figures.) 120.2 4 significant figures

The measurement 29.5 limits the number of significant figures in the answer to 3 significant figures.

The answer is 3.55 x 103 cm2; 3 significant figures.

Going back to the example in section 1.7, the answer is

3.85 x 103 cm2.

The answer has 3 significant figures because the length measurement is the measurement with the fewest significant figures (i.e. 3 significant figures). It limits the final answer to 3 significant figures.

Section 2.6
Mathematical Operations Involving Significant Digits ..p23

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