Complete Guide To Significant Figures: Number of Sig Figs and Rules For Addition And Multiplication

Rules on how to determine the number of significant figures?

1. All non-zero digits are significant. This means all numbers: 1,2,3,4,5,6,7,8, and 9 are significant. For example 5.67 has 3 significant figures.

2. All zeroes in between non-zero numbers are significant. For example zero in 303 is significant.

3. Leading zeroes (zeroes to the left of a number) are not significant. For example: 0.0009 has only one significant figure (9) since all of the zeroes to the left of it are not significant.

4. Trailing zeros to the right of a decimal point are significant. For example zeroes in 3.400 are significant.

5. Terminal zeros in a number without an explicit decimal point may or may not be significant (for example 300). To remove the confusion, we should write out these number using scientific notation (a written in another post)

Let's do some examples to figure out the number of significant figures:

675 = 3 significant figures

1.435 = 4 significant figures

809 = 3 significant figures

0.09 = 1 significant figure

2.0 = 2 significant figures

0.003400 = 4 significant figures

Significant Figures in Calculations

Addition And Subtraction

When adding or subtracting, round your answer to the same number of decimal places as there are in the number with the least decimal places.

For example, 89.332 + 1.1

The first number (89.332) has 3 decimal places while the second number (1.1) has 1 decimal place. 1.1 is the number with the least decimal places. Therefore, we should round our answer to 1 decimal place. 89.332 + 1.1 = 90.4

Multiplication and Division

When multiplying or dividing, round the answer to the same number of significant figures as the number with the least significant figures from your given.

For example, 2.8*4.5039

The first number has 2.8 has 2 significant figures and the second number, 4.5039 has 5 significant figures. 2.8 is the number with the least significant figures. Therefore, we should round the answer to 2 significant figures.

2.8*4.5039 = 13

Multistep Calculations

If there is a multistep problem, never round off your answer during a the process. Only round off at the very end!

If there is multiplication or division in your multistep process, even if there is addition and subtraction too, round the result to the same number of significant figures as the number with the least significant figures from your given.