Adding and Subtracting

In addition and subtraction, the number of significant figures in the answer depends on the number with the largest uncertainty.

Example

The measurement with the largest uncertainty is 152 g, and it is measured to the nearest gram. Therefore, the answer is given to the nearest gram.

Example

$189.427 \mathrm{g} - 19.00 \mathrm{g} = 170.427 \mathrm{g} \approx 170.43 \mathrm{g}$

The measurement with the larger uncertainty is 19.00 g, which is measured to the nearest hundredth of a gram. Therefore, the answer is given to the nearest hundredth of a gram.

Multiplying and Dividing

In multiplication and division, the measurement with the smallest number of significant figures determines the number of significant figures in the answer.

Example

$(5.3 \mathrm{m}) \times (1.54 \mathrm{m}) = 8.162 {\mathrm{m}}^2 \approx 8.2 {\mathrm{m}}^2$

Because 5.3 m has only two significant figures, the answer must be rounded to two significant figures.

Example

Because 5.5 mL has only two significant figures, the answer must be rounded to two significant figures.

Example

Calculate the perimeter [(2 × length) + (2 × width)] and the area (length × width) of a rectangular garden plot that measures 32.8 m by 16 m. Round each answer to the correct number of significant figures.

$\mathrm{Area} = 32.8 \mathrm{m} \times 16 \mathrm{m} = 524.8 {\mathrm{m}}^2 \approx 5.2 \times {10}^2 {\mathrm{m}}^2$