Place Value and How to Round Numbers

In a number, each digit's place tells you what it is worth. In 3,456, the 3 is worth 3,000, the 4 is worth 400, the 5 is worth 50 and the 6 is worth 6. Rounding swaps a number for a nearby, simpler one.

Try it with your own problem ↓

The steps

Name the places from the right: ones, tens, hundreds, thousands, ten-thousands, and so on. Decimals continue with tenths, hundredths and thousandths.
Find the digit in the place you are rounding to. This is the rounding digit.
Look at the digit just to its right.
If that digit is 5 or more, add 1 to the rounding digit (round up). If it is 4 or less, leave the rounding digit alone (round down).
Change every digit to the right of the rounding digit to 0. For a decimal, just drop them.

A worked example

Round 3,456 to the nearest hundred.

The hundreds place holds the 4, so 4 is the rounding digit.
The digit to its right is 5.
5 means round up, so the 4 becomes 5.
Change the digits after it to zeros: 56 becomes 00.

3,456 rounds to 3,500. It's between 3,400 and 3,500, and closer to 3,500.

Try it with your own problem

Open the free The Place Value Chart with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: round 3,456 to the nearest hundredOpens The Place Value Chart with this example

Or try these

Common mistakes

Looking at the wrong digit. Only the digit right next to the rounding place decides. For 3,449 to the nearest hundred, the 4 in the tens place decides, not the 9, so it gives 3,400.
Rounding twice. Don't round 3,449 up to 3,450 and then up again to 3,500.
Forgetting the zeros. 3,456 to the nearest hundred is 3,500, not 35.
Thinking 5 rounds down. The usual rule is that 5 rounds up.

Questions people ask

What is the rule for rounding 5?

In school math a 5 rounds up. (Some statistics courses round halves to the nearest even number, but a math class will tell you if that applies.)

What happens when the rounding digit is 9?

Rounding 396 to the nearest ten: the 9 goes up to 10, so write 0 and carry 1 into the hundreds, giving 400.

Why do we round?

To estimate, to check an answer quickly, and to report numbers in a way people can read, such as "about 3,500 people".

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