Estimation is important because it allows you to check that the answers you obtain on a calculator are reasonable. It is easy to make a simple mistake when using a calculator or working out a problem by hand, so an estimation of the expected answer is a useful check.

One of the simplest approaches to estimation is to round all the numbers involved to 1 significant figure.

(a)

Estimate the value of 4.73 × 18.4.

4.73 × 18.4 ≈ 5 × 20 = 100

(b)

Use a calculator to find 4.73 × 18.4.

4.73 × 18.4 = 87.032

(c)

Compare the estimate with the exact value.

Because in (a) we rounded both numbers up, the estimate is slightly bigger than the actual value, but it does give us an idea of the size of the answer.

The correct answer to 14.1 × 18.3 is listed below, along with 3 incorrect answers.

25.803

258.03

2580.3

25803

Use estimation to decide which is the correct answer.

14.1 × 18.3 ≈ 10 × 20 = 200

So the correct answer must be 258.03

Although we often round to 1 significant figure, we can sometimes produce better estimates by using other values that are still easy to work with. For example, in Example 2 above, we could have said that

14.1 × 18.3 ≈ 14 × 20 = 280

which is closer to the correct answer 258.03

The important thing to remember is that you must be able to do the estimation calculation *in your head*.

Estimate the value of:

(a)

≈ = = 2

or

≈ = = = = 2.6

Note that the actual value is 2.462 to 3 d.p.

(b)

≈ = = =

Note that is between 7 and 8, but will be closer to 7 since 7 = .

We can therefore take 7 as our estimate.

The actual value is 7.659 to 3 d.p.

You might also need to approximate when converting between different units. The following list reminds you of some of the important approximations between metric and imperial units.

8 km | ≈ | 5 miles |

1 m | ≈ | 40 inches |

30 cm | ≈ | 1 foot |

2.5 cm | ≈ | 1 inch |

1 kg | ≈ | 2.2 lbs |

1 litre | ≈ | 1.75 pints |

1 gallon | ≈ | 4.5 litres |

1 acre | ≈ | 0.4 hectare |

450 g | ≈ | 1 lb |