# Significant Figures Revision Notes

## What Are Significant Figures?

Significant figures (‘sig figs’ or ‘sf’) are a form of approximation similar to decimal places (‘dp’). The difference is that if you are rounding to 2dp, you start counting to 2 from the first digit after the decimal point. If you’re rounding to 2sf then you start counting from the first non-zero digit, whether this is before or after the decimal.

Sometimes this gives the same result:
``` 0.3456 to 3dp = 0.346 0.3456 to 3sf = 0.346```

However if the first digit after the decimal point is zero, you start counting sf from the first non-zero so things are different:
``` 0.03456 to 3dp = 0.035 0.03456 to 3sf = 0.0346```

Note that once you start counting digits for significant figures then you do count any zeros that come afterwards:
``` 0.0010203 to 3 dp = 0.001 0.0010203 to 3 sf = 0.00102 ```
If there are numbers before the decimal point, we start counting with them when using sf. This will usually give a totally different result to rounding to dp.
``` 1.05382 to 3dp = 1.054 1.05382 to 3sf = 1.05 2015639 to 3dp = 2015639 2015639 to 3sf = 2020000 ```
Note that with sig figs you must give exactly the number of digits asked for, even if this ends with one or more zeros:
``` 0.3102 to 3sf = 0.310 12.039 to 3sf = 12.0 1000099 to 3sf = 1000000 ```