Rounding whole numbers

Key points

When it’s not necessary to give an exact value, numbers can be rounded. Rounding means making a number simpler but keeping its value close to what it is.
When rounding numbers the result is less accurate, but easier to use. For example, if there were 39,828 spectators at a music concert the headline in a newspaper report might say 40,000 fans attended the event.
Depending on the size of the numbers, numbers can be rounded up or down to the nearest:
- whole number
- ten
- hundred
- thousand

Rounding Numbers

There are steps which can be followed to decide whether a number should be rounded up or rounded down.

Identify the in the column that you are rounding to. For example, if rounding to the nearest hundred then identify the digit in the hundreds place value column.
Leave the digit 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)
Using a as a representation is a useful way of visualising whether a number is closer to one value or another.
When using values on a number line, marking the halfway point can help to identify whether to round up or down.

Examples

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Image caption,
Use a number line to identify if you need to round up or round down. The whole numbers are equally spaced on this number line. The values increase by each step to the right.
Image caption,
Number lines can use different scales. The equally spaced steps here increase by 10 each time.
Image caption,
Marking the half way point between two values on a number line can help to identify whether to round up or down. For example, 75 is the halfway point between 70 and 80. Values below 75 will round down to 70. Values at 75 or above will round up to 80
Image caption,
Round 78 to the nearest ten.
Image caption,
Mark the value of 78 on the number line. This is between the values of 70 and 80. Keep the tens digit (7) and round the units digit. The units digit is 8 which is more than 5 so it is rounded up. 78 is closer to 80 than 70, so it is rounded up to 80. 78 rounded to the nearest ten is 80
Image caption,
Round 768 to the nearest hundred.
Image caption,
Mark the value of 768 on the number line. This is between the values of 700 and 800. Keep the hundred digit (7) and round the tens digit. The tens digit is 6 which is 5 or more so it is rounded up. 768 is closer to 800 than 700, so it is rounded up to 800. 768 is 800 when rounded to the nearest 100.
Image caption,
Round 14,368 to the nearest thousand.
Image caption,
Mark the value of 14,368 on the number line. This is between 14,000 and 15,000. Mark both values on the number line. 14,368 is a more difficult value to position on a number line, marking the half-way point of 14,500 can help. 14,368 is between 14,000 and 14,500. The number line shows that 14,368 is closer to 14,000 than 15,000. This means 14,368 should be rounded down to 14,000

A range of values

Sometimes you are given a rounded version of a number and need to explain what the original value was. In effect you need to work backwards.
Drawing a number line is a helpful representation to identify the minimum and maximum values that could have been used.
The number line should be increasing in the same sized step that the rounded value has been given to. (For example, if the rounded value is 70 to the nearest 10, then the number line should increase in steps of 10)

Examples

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Image caption,
The price of a meal is rounded to the nearest £10 to cost £40. What different amounts could the original bill have been?
Image caption,
Draw a number line with the value of £40 identified.
Image caption,
The value was rounded to the nearest £10, which means the equal spaced steps on the number line should increase (and decrease) by 10 each time.
Image caption,
Mark the halfway point between 30 and 40 (which is 35). Mark the halfway point between 40 and 50 (which is 45).
Image caption,
All amounts which are £35 or above will be rounded up to make £40
Image caption,
All amounts below £45 will be rounded down to make £40. Remember that 45 would be rounded up to £50
Image caption,
The original bill could have been any amount that is either £35 or above up to but NOT including £45. A different way of writing this could be £35 or above up to £44.99

Question

Which of these numbers when rounded to the nearest hundred give 11,600?

Eleven-thousand six-hundred and sixty-nine. Eleven-thousand five-hundred and fifty. Eleven-thousand six-hundred and one. Eleven-thousand seven-hundred and one.

Practise rounding whole numbers

Practise rounding whole numbers in this quiz.

Quiz

Real-world maths

Checking a receipt for shopping in a supermarket trolley. — Image caption,
Rounding the value of items when shopping can be a quick way of making sure you don't overspend.

Rounding whole numbers is used regularly in everyday life.The exact figure or value is not always needed initially, particularly if people are deciding whether they can afford a product or not.

When shopping people often round the value of items they are buying to the nearest £1 and add them together to make sure they don’t over-spend.
Newspapers and magazines may round the attendance at sporting events or festivals to the nearest thousand or ten thousand in their headlines, rather than printing the actual attendance. This makes it easier for the audience to read and remember.

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Key points

Rounding Numbers

Examples

A range of values

Examples

Question

Practise rounding whole numbers

Quiz

Real-world maths

Game - Divided Islands

More on Rounding and estimating

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Key points

Rounding Numbers

Examples

A range of values

Examples

Question

Show moreShow less

Practise rounding whole numbers

Quiz

Real-world maths

Game - Divided Islands

More on Rounding and estimating

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