Decimal Places And Significant Figures

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)

Significant figures and decimal placesSo 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.example questionsHere’s a bunch of example questions. To reveal the answer click on the “answer” tab.

What is 8.78549 to 2 d.p.
Round 5.1686 to the nearest tenth

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

4.992 to 2
6410.58 to 3 significant figures
0.006645204 to 5 significant figures.

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