Unit 4 Section 6 : Estimating

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.

Example Questions

(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

 

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer 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?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
A box of matches contains 52 matches.

Estimate the total number of matches in 8 boxes.
Give your answer to 1 significant figure.
matches

Question 2
The floor of a room measures 3.8m by 4.1m.

Estimate the area of the room in m².
Give your answer to 2 significant figures.
m²

Question 3
25 drink cans cost 59p each.

Estimate the total cost of the cans.
Give your answer in pounds (£) to the nearest pound.
£

Question 4
Kyle uses his calculator to do the calculations listed below, and gives his answers correct to 3 decimal places.

Using estimates to check, decide which of Kyle's answers are definitely incorrect.
(a) 36.41 × 37.32 = 135.882
(b) 56.2 × 1.97 = 11.071
(c) 82.3 × 0.625 = 51.438
(d) (204 + 109) × 10.2 = 3.193
(e) (16.7 + 31.3) ÷ 4.75 = 1.011

Question 5
A school purchases 194 calculators at a cost of £8.16 each.

Estimate the total cost of the purchase.
Give your answer to the nearest £100.
£

Question 6
A can contains 584 millilitres of drink. A box contains 26 cans.

Estimate the total volume of drink in a box.
Give your answer in litres, to the nearest litre. litres

You have now completed Unit 4 Section 6
Your overall score for this section is
Correct Answers
You answered questions correctly out of the questions in this section.
Incorrect Answers
There were questions where you used the Tell Me button.
There were questions with wrong answers.
There were questions you didn't attempt.
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