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# 3.4 Did I make a rough estimate to act as a check?

When using a calculator many people have ‘blind faith’ in its capacity to provide the correct result.

Calculators invariably provide the correct result for the information they are given; any errors are due to the operator.

To help guard against errors, always give a ‘ball-park’ estimate for a problem, using rounded values and easy calculations.

For example, make a rough estimate of the calculation below to act as a check upon the actual calculation using the calculator.

3.421 + 5.986 + 12.009 87 = ?

Rough check: 3 + 6 + 12 = 21

Calculator answer: 21.416 87

The two answers are within the same ‘ball-park’ so you should be happy with the calculator's answer. Had you got an answer of 3438.995 87, say, you should be suspicious and checking would reveal you had missed out a decimal point.

It is helpful to adopt this checking strategy for all your calculations since it is so easy to press the wrong key inadvertently, or double press a key when working at speed on a calculator.

Often it is useful to have both an underestimate and an overestimate.

## Example 11

Look back at Example 9, which gave an incorrect answer. How could you have spotted this without doing the whole calculation?

### Answer

First do an overestimate, then an underestimate, per person.

In an overestimate, ignore the float and round the food up to £40, drinks to £6, taxi £4, tip £3 minus £5 discount gives £48 this is less than £50. Divide by 5 people means the maximum share for each person is £10. Hence £10.80 is too much.

An underestimate would be £35 for food, £5 for drinks, £3 for taxi and £3 for tip, less £5 for the voucher and £1 float. This gives £40, divided by 5, which means minimum of £8 each.

Hence you would expect an answer between £8 and £10.

One common error when using a calculator is to forget that the calculator does not total everything as it goes along. So, for example, in the case of the bill for a night out, you must total everything before you divide by the number of people who are sharing the bill.

## Example 12

Look back at Example 8 and suppose that the calculation was put into a scientific calculator, in the following form:

0.04 + 5.00 + 8.00 − 36.98 − 5.10 − 3.50 − 3.00 ÷ 4 = ?

Would this give the right answer?

### Answer

No, it would not give the right answer. The calculator will do the division first, i.e. 3.00 ÷ 4, and then all the additions and subtractions, to give the answer −32.93. And £32.93 is clearly too much for each person's share of the bill.

In order to make it do the calculation correctly, you can either total after the 3.00, by using the ‘=’ (or ‘ENTER’) button, or use brackets.

(0.40 + 5.00 + 8.00 − 36.98 − 5.10 − 3.50 − 3.00) ÷ 4

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OpenLearn - Rounding and estimation
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