Chemistry and Measurements - Significant Figures in Calculations

Significant Figures in Calculations

Rounding Off

  • Calculated answers are usually rounded off.
  • Rounding rules are used to obtain the correct number of significant figures.

Rules for Rounding Off

  • If the first digit to be dropped is 4 or less, then it and all the following digits are dropped from the number.
  • If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1.
Examples of Rounding Off
Number to Round OffThree Significant FiguresTwo Significant Figures
8.42348.42 (drop 34)8.4 (drop 234)
14.78014.8 (drop 80, increase the last retained digit by 1)15 (drop 780, increase the last retained digit by 1)
32563260* (drop 6, increase the last retained digit by 1, add 0) 3.26×1033.26 \times 10^33300* (drop 56, increase the last retained digit by 1, add 00) 3.3×1033.3 \times 10^3
  • The value of a large number is retained by using placeholder zeros to replace dropped digits.

Learning Check 1

Write the correct value when 3.145 g is rounded off to each of the following:
A. three SFs
B. two SFs

Solution 1

A. To round off 3.145 to three SFs,
* drop the final digit, 5
* increase the last remaining digit by 1
The answer is 3.15 g.
B. To round off 3.145 g to two SFs,
* drop the final digits, 45
* do not increase the last number by 1 since the next digit is 4
The answer is 3.1 g.

Learning Check 2

Adjust the following calculated answers to give answers with three significant figures:
A. 824.75 cm
B. 0.112 486 g
C. 5.3 L

Solution 2

A. 824.75 cm 825 cm
B. 0.112 486 g 0.112 g
C. 5.3 L 5.30 L

Multiplication and Division With Measured Numbers

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

Adding Significant Zeros

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

Learning Check 3

Perform the following calculation of measured numbers. Give the answer with the correct number of significant figures.

Solution 3

Perform the following calculation of measured numbers. Give the answer with the correct number of significant figures. Using a calculator: Express answer with 2 SFs and proper units:

Addition and Subtraction With SFs

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.

Example 1: Addition

Add the following measured numbers:

  1. 012 Thousandths place
  2. 09 Hundredths place
  • 3.0 Tenths place

66.102 Calculator display
66.1 Answer rounded to the tenths place

Example 2: Subtraction

Subtract the following measured numbers:

  1. 09 Hundredths place
    negative 3.0 Tenths place

62.09 Calculator display
62.1 Answer rounded to the tenths place

Learning Check 4

Add the following measured numbers:

Solution 4

Add the following measured numbers:

  1. 409 mg Thousandths place
    +22.0 mg Tenths place

  2. 409 mg Calculator display

  3. 4 mg Answer rounded to the tenths place