# Rounding Up and Down

Rounding is surprisingly complicated for some people; the rule is straightforward but I constantly encounter children who cannot put all the pieces together accurately.

If you round a number, you effectively estimate it. For example, 51 is nearly 50, 4.2 is nearly 4 and so on. The rule, which all children can recite, is that 5, 6, 7, 8 and 9 get rounded up, the rest get rounded down. However, there are things to bear in mind.

Numbers get rounded to the nearest whole number, the nearest 10, the nearest 100... Occasionally they could be rounded to the nearest multiple of a given number. The likelihood is that your child will get a question on an entrance paper which uses decimals as well - they are only slightly more difficult in reality.

Let's look at a simple question:

What is 4.49 to the nearest whole number?

The answer is 4. It should be presented as just the digit 4, not 4.00 nor 4.0 as it is simply a whole number.

The process is to look at place value and decide which digits can remain, which must be adjusted and which removed altogether. If the number must be rounded to the nearest whole number, the UNITS column of the answer will either remain as it is * (rounding down) * or it will increase by one * (rounding up) *. This will be determined by the TENTHS column, as this is the next column to the right from the units. The tenths column itself - and everything to the right of it - will disappear in your answer.

In our example, the place value set-up looks like this:

UNITS | . | TENTHS | HUNDREDTHS |

4 | . | 4 | 9 |

The units (whole numbers) are the only thing that will exist once we've rounded. The answer must be 4 or 5 as the full number we have is between 4 and 5. Rounding down does NOT allow for dropping below the value of the digit.

If we had to round 2,568 to the nearest thousand, the answer would be 3,000. We look at the THOUSANDS column and decide whether it remains as it is *(rounding down) * or increases by one *(rounding up) *. This is determined by the next column to the right of the thousands - the HUNDREDS. As it is '5', and all digits between 5 and 9 round up, we must round the thousands column up to 3. All the remaining digits to the right will become zeroes. This is critical and is often forgotten by children.

Sometimes we encounter values to the left of the column being 'rounded'. For instance, 917,022 to the nearest thousand is 917,000. The thousands column stays at '7' as the following column is '0'; also, it is the last one which is allowed to have any digits in it other than 0.