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.

Answer:

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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