Bitesize has changed! We're updating subjects as fast as we can. Visit our new site to find Bitesize guides and clips - and tell us what you think!

Home > Maths > Number > Approximation

Maths

Approximation

Print

Trial and improvement

When using trial and improvement guess what the answer might be, then improve on it until you get close to the correct answer.

Example

A square has an area of 20 cm2. Use a method of trial and improvement to find the length of its side, correct to 1 decimal place (1 d.p.).

  1. Start by trying 4:

    4 × 4 = 16 (too small)

  2. 4 is too small, so try 5:

    5 × 5 = 25 (too big)

  3. 4 is too small, and 5 is too big, so the answer lies between 4 and 5.

    Try 4.5:

    4.5 × 4.5 = 20.25 (too big)

    Try 4.4:

    4.4 × 4.4 = 19.36 (too small)

Therefore, the answer lies between 4.4 and 4.5, but it is closer to 4.5.

So the answer is 4.5cm to 1 d.p.

More accurate answers

The question asked us to find the length of the side correct to 1 d.p., so you only need to try values with 1 d.p.

If, however, the question had asked for values correct to 2 d.p. you would have got a more accurate answer. For example:

4.45 × 4.45 = 19.80 (too small)

Activity

Approximation activity

Round up, round up and try this activity!

Play

Elemental

Can you conquer the elements?

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.