Significant Figures

Numbers are often rounded to avoid reporting insignificant figures. Significant figures are often used in connecting with rounding.

Rounding 15.543 or 4.756 to 1 decimal place (d.p) seems sensible. The rounded figure is very close to an actual value.

15.543 = 15.5 (1 d.p)

4.756 = 4.8 (1 d.p)

But what happens if you round a very small number to 1 d.p?

0.00789 = 0.0 (1 d.p)

0.00456 = 0.0 (1 d.p)

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:

0.0067 (Here, 6 is the first significant figure and 7 is the second significant figure)

0.0508 From the first significant figure onwards, all zeros are included. It's only the zeros at the beginning that don't count. Here, 5 is the first significant figure, 0-second significant figure and 8 is the third significant figure.

Examples

1. Round 0.0724591 to 3 significant figures, look at the fourth significant figure. It's a 5, so round up.
   0.0724591
   Therefore, 0.0724591 = 0.0725 (3 s.f.)
   
   
2. Round 0.2300105 to four significant figures.
   Solution:
   To round to four significant figures, look at the fifth significant figures.It's a 1, so round down.
   0.2300105
   Therefore, 0.2300105 = 0.2300 (4 s.f)
   Even though 0.2300 is the same as 0.23, include the zeros to show that you have rounded to 4 significant figures.