What is estimating?

Key points

It is not always easy or necessary to give an exact value, so can be made.
Estimating is a way of making a calculation more manageable. For example, if you were going to buy 12 items that cost £28.99 each then an estimate of the total might be £300 (rounding both numbers to the nearest 10 is 10 lots of £30).
As there isn't one set way to estimate, people might round their values in slightly different ways.
A number can be rounded in different ways depending on its size. For example, to the nearest:
- whole number
- ten
- hundred
- thousand

Estimating Values

Estimating means making numbers simpler but keeping their value close to what it was. The result is not exact, but it gives an idea of what the total will be.

There are steps which can be followed to decide how to round a value to make it easier to deal with.

Find the most important digit in the value you have been given. This is usually referred to as the most .
Establish what place value column the most significant figure is positioned. Round the value to that degree of .
Refer back to the rules of rounding to decide whether this value should be rounded up or down.
Leave it the same if the next digit is less than 5 (this is called rounding down).
But increase it by 1 if the next digit is 5 or more (this is called rounding up).

Examples

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What value could be used as an estimate for £12.95?
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Identify the most significant figure in the amount. The most significant figure in £12.95 is the digit 1, as it is in the highest place value column.
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A good estimation for £12.95 would be to round to the nearest £10. Rounding to the nearest £10 generally produces an easy value to deal with. £12.95 rounded to the nearest 10 is £10
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There isn’t one set way to estimate. A different way to estimate could be to round to the nearest £1. £12.95 rounded to the nearest £ would be £13. Whilst both are correct, estimation is used to make the calculations easier.
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A builder will take 31 days to complete construction work. The builder works for 9 hours per day. The cost of labour is £12.95 per hour. Estimate the total cost of the construction.
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Round the 3 values to make the calculation easier to manage and provide a rough guide to the total cost. The total number of days has been rounded down to 30 days. The number of hours per day has been rounded up to 10. The cost of labour has been rounded down to £10 per hour.
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Work out the total estimated cost. 10 hours per day at £10 per hour gives a total of £100 per day (10 x £10). 30 days of labour at £100 per day means that the total estimated cost is £3,000 (30 x £100).
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Work out the actual total cost. 9 hours per day at £12.95 per hour gives a total of £116.55 per day (9 x £12.95). 31 days of labour at £116.55 per day means that the total cost is £3,613.05 (£116.55 x 31). This is slightly more than the estimated cost of £3,000

Comparing different prices

People often make decisions about what offer might provide the best value for money. This could be when choosing between two different sized boxes of cereal in a supermarket or deciding which mobile phone contract is offering better value for money.
Using estimation can help people to make more informed decisions about which product or offer would represent the best value.

Examples

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Image caption,
Which offer for a 12-month mobile phone contract has the best value for money?
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Two different phone companies have an offer for a new smartphone. The contracts are both for 12 months and they have the same amount of data and calls per month. One has a lower upfront cost but a larger monthly repayment. Which one will be the best value for money overall?
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Look at the offers individually, starting with Company 1. Round the values that are given to the nearest ten. £38 rounded to the nearest ten is £40. £28.95 rounded to the nearest ten is £30
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Work out the total estimated cost. The total estimated cost is the monthly repayments + the upfront cost. 12 (months) x £30 = £360. £360 + £40 = £400. The total estimated cost for company 1’s contract is £400
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Look at the offer for company 2. Round the values that are given to numbers that are easy to work with. £115 can be rounded to £100. £21.75 can be rounded to £20
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Work out the total estimated cost. The total estimated cost is the monthly repayments + the upfront cost. 12 (months) x £20 = £240. £240 + £100 = £340. The total estimated cost for company 2’s contract is £340
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Company 1’s total estimated cost is £400. Company 2’s total estimated cost is £340. Using estimated values, it looks like buying the phone from company 2 could be better value for money. When estimating in real-life, always check the exact amount to make sure you are getting the best value for money.

Question

A shop wants to buy 78 boxes of cereal from the wholesaler. Each box costs £1.08. Estimate the total cost of this order.

Practise estimating

Practise estimating with this quiz.

Quiz

Real-world maths

Estimating numbers is used regularly in everyday life. It is used to make calculations more manageable.

In the video, we see how estimation can be used by a catering company to predict the amount of ingredients needed for an event:0.75 kg of tomatoes are needed for 10 people.

To estimate how much produce to buy for the full party of 70 people, we need to multiply 0.75 by 7:0.75 × 7 = 5.25 kg

This tells us that we need at least 5.25 kg of tomatoes. The manager adds an extra 10% on to the total in case some of the tomatoes are squashed or damaged, and rounds up to 6 kg.

This is only an estimate as it is not always possible to predict exactly how many tomatoes are required.

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Watch this film to see how an events manager uses estimating for a large scale event.

Key points

Estimating Values

Examples

Comparing different prices

Examples

Question

Practise estimating

Quiz

Real-world maths

Game - Divided Islands

More on Rounding and estimating

Key points

Estimating Values

Examples

Comparing different prices

Examples

Question

Show answerHide answer

Practise estimating

Quiz

Real-world maths

Game - Divided Islands

More on Rounding and estimating