Significant figures

Another way of rounding numbers is to count only the first few digits (maybe 1, 2 or 3 figures) that have a value attached to them. This method of rounding is called significant figures and it’s often used with larger numbers, or very small numbers.

Rounding 12.756 or 4.543 to one decimal place seems sensible, as the rounded figures are roughly equal to the actual value.

12.756 = 12.8 ( 1 decimal place)

4.543 = 4.5 ( 1 decimal place)

But what happens if you round a very small number to one decimal place?

0.00546 = 0.0 ( 1 decimal place)

0.00213 = 0.0 ( 1 decimal place)

This is not a useful answer. Another way to find an approximate answer with very small numbers is to use significant figures.

Counting significant figures

Significant figures start at the first non-zero number, so ignore the zeros at the front, but not the ones in between. Look at the following examples:

Diagram of the number 0.0071Diagram of the number 0.0345Diagram of the number 0.00702 showing the 1st, 2nd and 3rd significant figuresDiagram of the number 72,800 showing the 1st, 2nd and 3rd significant figures
From the first significant figure onwards, all zeros are included. It's only the zeros at the beginning that don't count.

How many significant figures do the following numbers have?

a) 0.3007

b) 2.01

c) 0.001023

d) 37,500

a) 0.3007 has four significant figures.

b) 2.01 has three significant figures.

c) 0.001023 has four significant figures.

d) 37,500 has three significant figures.