## Rounding Decimals

#### Introduction

Rounding decimals is a useful tactic when it comes to making numbers easier to work with. For example, if we are given the number:

$5.092196765765$

We might decide to just round it to 5.1 to make it more manageable for our sums. Knowing how to round decimals means know whether to round it up or down so that, even though we're making this simpler, we are still being as accurate as possible.

#### Terms

**Decimal Point**- The decimal point looks like a period and is always placed after the “ones” position of a number.

**Decimal Notation**- Decimal notation is useful for writing numbers which are not whole numbers.

**Whole Number**- A whole number is a number with nothing but zeroes after the decimal point.

## Lesson

When we decide to round a number, the first question to ask is 'how many digits do we need?' If we're measuring the distance from the Earth to the Sun, it is unlikely that we will need to measure to the hundredths of an inch. If we're measuring the length of a grain of rice, we will need to be precise to the thousandth or ten-thousandth of an inch.

The rule of rounding is that you take the number of digits you want and then look at the next one. If the next column is 5 or higher, you round up your number. If the next column is less than 5, you round down.

Once we've decided how accurate we need to be, we can start to round and remove numbers. For example, let's say we're working with the number:

$82.197362$

Tens | Ones | . | Tenths | Hundredths | Thousandths | Ten-Thousandths | Hundredth-Thousandths | Millionths |
---|---|---|---|---|---|---|---|---|

8 | 2 | . | 1 | 9 | 7 | 3 | 6 | 2 |

If we decide that we want to round the number to the tenths, we can see that the number is 82.1. However, if we look to the hundredths column, that is a 9, so we will need to round the tenths column up to 2. We can then write the number as 82.2

If we want to know the same number to the thousandths, we can write it as 82.197. Looking to the next column along, we can see that it is a 3, which gets rounded down, so the number stays at 82.197.