Calculating the number of significant figures in a number is a relatively simple process, but it depends on a clear understanding of four main rules. The examples below set out the guidance for each rule and provide various examples to help you understand how the calculation is being made in each case. Should you wish to check your calculations at any point, you can use our sig figs calculator.
This is a fundamental rule and the easiest to understand. Any non-zero digit in a number must be considered as significant.
If a zero forms part of a string of digits AND falls between two non-zero digits then it must be counted as a significant figure.
Where there are leading or trailing zeroes in a number, there are some other factors which come into play, specifically around the placement of the zeroes relative to any decimal point and other digits.
Any leading zeroes are never significant, irrespective of a decimal point
Zeroes contained before or after a decimal point are considered as significant figures if they fall between two non-zero digits, as per rule 2, OR potentially when they are trailing, not leading zeroes. Trailing zeroes are only counted when a decimal point is included in the number, as shown below.
This is the hardest rule to grasp and requires various examples to explain.
These four basic rules will help determine the number of significant figures in any number. However if you wish to do mathematical calculations and still work out the number of significant figures then a new set of rules comes into play! These rules also differ depending on whether you are combining numbers in an addition or subtraction, or performing multiplication or division.
Note in this case that if we had been asked to subtract 1.55 from 3.20 (the trailing zero being significant) the answer can have two significant figures and would be correctly deemed to be 1.65!
Unlike the addition and subtraction example, you now must calculate the number of significant figures in each number in its entirely before performing the calculation, not just the decimal part. Once you have performed the calculation, the answer now must contain the same number of significant figures as the smallest total of them in the initial numbers.
a) multiply 3.1 by 3.5
Each number has two significant figures therefore the answer can have a maximum of two significant figures.
3.1 x 3.5 = 10.85
However 10.85 has four significant figures and therefore must be rounded to 11, which has two. So in this case the correct answer is 11.
b) multiply 3.10 by 3.50
Each number has three significant figures, so the answer can have a maximum of three.
3.10 x 3.50 = 10.85
Again, round this number appropriately to create an answer with three significant figures - in this case the answer is now 10.9!
c) multiply 3.100 by 3.500
Each number in the question has four significant figures and therefore the answer must too.
3.100 x 3.500 = 10.85
This answer (10.85) has four significant figures and therefore remains the correct one to use.
These examples cover many of the most common types of significant figure calculations and should help you answer questions on this topic. It's important to learn the rules around zeroes and particularly the difference between calculations involving addition/subtraction and multiplication/division as this is where most errors occur.
For help with calculating and counting significant figures, you can use our significant figures calculator.
Written by Paul Meehan, PhD chemistry