Rounding involves simplifying numbers, to make them easier to work with, for example when estimating. Numbers can be rounded to the nearest ten, hundred or thousand, for example, or to a fixed number of decimal places.

Rounding process

Numbers are rounded up or down to the chosen place value, depending on the digit to its right.

If the digit to the right is

• 5 or above, round up: Increase the digit in the 'rounded' column by 1, and replace the digit(s) to the right with 0.
• Less than 5, round down: Leave the digit in the 'rounded' column as it is, and replace the digit(s) to the right with 0.

Let's look at an example.

Round 2270 to the nearest 100.

Th	H	T	U
2	2	7	0

The digit to the right of the hundreds column is 7.

This is higher than 5 so we round up.

The digit in the hundreds column (2) becomes 3.

The digits in the columns to the right become 0.

2270 rounded to the nearest 100 is 2300.

Try it out

Round 45037 to the nearest thousand.

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Rounding to decimal places

When you are working with money, you will always work to two decimal places. For other decimals, with lots of numbers to the right of the decimal point, you may wish to simplify these to a certain number of places.

The process is similar to that described above for whole numbers, however when rounding has taken place, the digits to the right of the decimal place are discarded.

For example, if you are rounding to two decimal places, look at the third digit to the right of the decimal point.

If it is

• 5 or more, increase the second decimal place digit by 1, and discard the digit(s) to the right.
• less than 5, leave the second decimal place digit as it is, and discard the digits to the right.

Let's look at an example.

Round 22.325796 to one decimal place.

22.3

25796

The digit to the right of the first decimal place is 2, which is less than 5 so we round down.

The first decimal place digit (3) remains the same and the digits after this are discarded.

22.325796 becomes 22.3 when rounded to one decimal place.

Try it out

Round 37.5275894 to two decimal places.

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Rounding and estimating

Rounding is useful for estimating, for example when you are shopping.

As you add items to your basket, it is easier to keep a running tally in your head if you round prices to the nearest pound.

For example,

Item	Price	Rounded to	Running total
1	£0.99	£1	£1
2	£1.79	£2	£3
3	£0.43	£0	£3
4	£0.67	£1	£4

So the estimated cost of the items in the basket so far is £4.00.

The actual cost is £3.88, so not a bad estimate!

Try it out

Estimate the cost of these items as you add them to your shopping basket by rounding them to the nearest pound and keeping a tally of the rounded prices as you go.

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