Significant Figures in Calculations: Multiplication, Division, Addition, and Subtraction

Significant Figures in Calculations

Multiplication and Division

When performing multiplication or division with measured values, the number of significant figures in the final answer should match the measurement with the fewest significant figures.

• Significant figures are the digits in a number that carry meaning contributing to its precision.

• To determine the correct number of significant figures, identify the measured value with the least number of significant figures in the calculation.

Example: Perform the following calculation to the right number of significant figures: $1.8 \times 0.0357 \times (87.4 - 1.9) \div 2.015 = 3.5$ (2 sig figs)

Addition and Subtraction

When adding or subtracting measured values, the number of decimal places in the final answer should match the measurement with the fewest decimal places.

• Count the number of decimal places in each measured value.

• The answer should be rounded to the least number of decimal places present in any of the numbers.

Example: Perform the following calculation to the right number of significant figures: $210.9 - 212.2 = -1.3$ (rounded to 1 decimal place)

Mixed Operations

When a calculation involves both multiplication/division and addition/subtraction, follow the order of operations and apply the significant figures or decimal places rule at each step.

• First, perform operations inside parentheses and apply the appropriate rule for each step.

• Carry extra digits through intermediate steps and round only the final answer.

Example: Perform the following calculation to the right number of significant figures: $(8.12/2) - 6.5) \times (2.920 + 1.11)$

• Step 1: $8.12 \div 2 = 4.06$

• Step 2: $4.06 - 6.5 = -2.44$

• Step 3: $2.920 + 1.11 = 4.03$

• Step 4: $-2.44 \times 4.03 = -9.8$ (rounded to 2 sig figs)

Practice Problems

• Practice 1: $3.7 \times 10^2 \times (2.63 \times 10^1) \div 6.98$ Answer: $1.4 \times 10^2$

• Practice 2: What answer should be reported, with the correct number of significant figures, for the following calculation? $42.00 - 40.815$ $11.503 \times 1.001$ Answer: $0.0862$

Summary Table: Rules for Significant Figures

Operation	Rule	Example
Multiplication/Division	Result has the same number of significant figures as the value with the fewest significant figures.	$2.5 \times 3.42 = 8.6$ (2 sig figs)
Addition/Subtraction	Result has the same number of decimal places as the value with the fewest decimal places.	$12.11 + 18.0 = 30.1$ (1 decimal place)