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# Decimals

## Significant Figures

Significant figures give an idea of the accuracy of a number.  Imagine having two tape measures, one with markings every decimetre

and the other with the millimetres marked.  The second can make a more accurate measurement than the first.  We can use significant figures to show the difference.

The first might report the length of this pool at 25.0 metres, meaning that the length is closest to the marking 25.0 metres on the measuring tape.

The second is much more accurate so might come up with a length of 25.008 metres, meaning that it finds the length to be closest to the 25.008 metres mark on the measuring tape.

Placeholders, or digits that have not been measured, are not considered significant. For example, in a measurement of 0.0123 L the leading two `0`s are placeholders and therefore are not significant. All other digits are significant.

## Zeros

If a decimal number starts with a string of "0" we call these "0"s the leading "0"s and if it ends with a string of "0" we call them trailing "0"s.

For example,

### Rules for significant figures:

1. If the number has a decimal point, the leading "0"s are not significant. All other digits (including trailing "0"s) are significant.
2. If the number is a whole number, the trailing "0"s are not significant. All other digits (including "0"s) are significant. If some of the trailing "0"s are to be considered significant, we should write them in scientific notation to show this.

150.0 has 4 significant figures whereas we are uncertain as to whether 150 has 2 (150) or 3 (150). The only way to be certain is to write the number in scientific notation.

1.5 x 102 has 2 significant figures whereas 1.50 x 102 has 3 significant figures.

To be clear we say:

The number 1300 has 2 s.f.,
While 1.30 x 103 has 3 s.f. and 1.300 x 103 has 4 s.f..

### Examples

 Number 0.00109 0.1 2300 807 2003 1.00002 1000 Sig. Fig. 3 4 2 5 4 6 1

### Exercise

 has significant figures.