Decimal places and their trickier cousins significant figures both tell you the how accurately a number should be written. We don’t always need to know the absolute exact number and can sometimes settle for an approximation.

### Decimal Places

You might be asked in an exam to express a number to a certain number of decimal places. Keep calm and just follow his process.

- Identify the last digit from the number of decimal places asked for. So if you need to find a number to 2 d.p. just take the second number after the dot.
- Look to the number to the right of this one. If it is 5 or above, round the last digit up, below 5 round it down
- If the last digit is a 9 and you have to round it up, replace it by a 0 and add one to the second to last number

So for example round 32.799 to 2 d.p.

The answer is 32.80

### Significant figures

When dealing with questions involving significant figures there are just a few things you need to remember.

- The first significant figure is just the first number that isn’t a zero
- All the numbers after this are significant, even if they are a zero
- After rounding up the last significant digit, fill in zeros (but not beyond the decimal point)

So here’s some examples:

0.045 to 1 s.f. is 0.04

1.567 to 3 s.f. is 1.57

20894.5 to 2 s.f. is 21000

1.454 to 3 s.f. is 1.45

You might be asked to estimate a value for an equation during a non-calculator paper. In such a case just use your common sense to get a reasonable degree of accuracy (usually 1 or 2 s.f.).

### Finding The Bounds

When a measure is rounded to a given unit (e.g. 2 d.p.) then the actual measure could be half a unit bigger or smaller.

So let’s take an example:

If a fence was 10.5cm by 5.6cm to the nearest tenth of a cm, what are the bounds of its area?

The minimum value for the area is 10.45cm x 5.55cm = 57.9975 cm squared

The maximum value for the area is 10.55cm x 5.65cm = 59.6075 cm squared.**Here’s a bunch of example questions. To reveal the answer click on the “answer” tab.**

The first digital after the decimal point is called a tenth. The second is a hundredth, the third a thousandth etc.

Remember the first significant figure is the first number that isn’t a zero.