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Approximation

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# 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.

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)

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