The best way to estimate the answers to calculations without a calculator
is to round the numbers sensibly and then carry out the calculation by hand.
Often, the numbers in the question can just be rounded to 1 significant figure, but
sometimes this is a bit excessive, so you need to choose a sensible level of rounding.
You can use estimates to help check your answers to questions done using a calculator.
This is done by following these steps:
1. ESTIMATE the answer mentally.
2. CALCULATE the answer on the calculator.
3. CHECK the calculator answer is a similar size to your mental estimate.
(a) Estimate the cost of 21 packs of screws each costing £2.90.
The actual calculation is 21 × 2.9.
If we round the numbers to 1 significant figure we get 20 × 3, which we can do without a calculator.
Our estimated answer is £60 (which is quite close to the actual answer of £60.90).
(b) Estimate the length of 29 pieces of wood layed end-to-end if each is 1.48m long.
The actual calculation is 29 × 1.5.
If we round the numbers to 1 significant figure we get 30 × 1.
The estimated answer using 1 significant figure is 30m (which is quite different to the actual answer of 42.92m).
In this case, we need to be sensible about the rounding, for example we could calculate 30 × 1.5.
The estimated answer using more sensible rounding is 45m (which is much closer to the actual answer).
(c) James has worked out 31.5 × 49.6 and got the answer 156.24.
Use estimation to check whether his answer is likely to be correct.
If we round the numbers to 1 significant figure we get 30 × 50.
The estimated answer using 1 significant figure is 1500m (which is very different to the answer James got).
James has probably got the decimal point in the wrong place - the answer should be 1562.4
Work out the answer to each of these questions then click on the button marked to see whether you are correct.
(a) Estimate the weight of 38 boxes each weighing 26 kg.
(b) Jane has calculated 3.88 × 16.1 and got 62.468. Does her answer seem correct?