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# Rounding Decimals

Rounding with decimals is usually required after a calculation or a measurement. After a calculation, knowing whether to round up or down is very dependent on circumstances.For example, if you calculate that you need 4.2 vehicles to carry a group of people then would need to round up. If, on the other hand, you calculated that you had enough money to buy everyone 2.8 drinks, then you would need to round down. There are more examples below.

Note: You will find rounding decimals worksheets listed at the foot of this page.

### Rounding Examples

Example 1: It costs $1.25 to download a song. You have$12.00. How many songs can you download?

Solution: Divide $12.00 by$1.25 to get 9.6 songs. We will not be able to buy .6 of a song (just a bit of a song). In this case we need to round down to get an answer of 9 songs

Example 2: The floor area of a room is 100 square feet. The floor is to be replaced with hardwood which comes in packs of 16 square feet. How many packs are required?

Solution: Divide 100 sq. ft. by 16 sq. ft. to get 6.25 packs of hardwood. We cannot buy .25 of a pack so we need to round up to find that 7 packs are required.

### Rounding decimals questions

Rounding decimals questions will usually be asked in one of two ways; to the nearest tenth, hundredth, or thousandth, or to one, two, or three decimal places “One decimal place” is the same as “the nearest tenth”. “Two decimal places” is the same as “the nearest hundredth”. “Three decimal places” is the same as “the nearest thousandth.”

So, for example, if you are asked to round 3.264 to two decimal places it means the same as if your are asked to round 3.264 to the nearest hundredth.

Some questions, like the example below, will ask you to “show your answer correct to two decimal places.”

## How to Round Decimals – Decomposing the Number

Writing numbers in their expanded form and decomposing them using different units as shown below can help when rounding to different places.

We will use the decompositions in bold to round these three numbers. The first one, 134, does not have a decimal part but illustrates the technique and how understanding place value helps when rounding numbers.

A vertical number line is useful for many students as it supports visually the concept of “up or down”. The examples that follow use the more common horizontal line. Ensure your children are comfortable with this transition and provide extra practice if required. There are several horizontal and vertical number lines here.

## How to Round Decimals – On a Number Line

With language like “to the nearest” it is not surprising that a good way to visualize rounding is by showing decimals on a number line. The three examples below use number lines to illustrate rounding of decimals.

### Rules for rounding

You can round decimals without the help of a number line using the steps as shown in the example below

The examples below show how the steps above can be applied when rounding to the nearest whole number, nearest tenth, and nearest hundredth.

## Example Showing Rounding to the Nearest Hundredth

You can use the Rounding Calculator below to check your answers and also to try some more examples for yourself.

## More on Rounding Decimals

Problems like the example below can sometimes be a little trickier. They require a good understanding of decimal place value.

Do not round in stages as the example below shows.

Example: When rounding 4.648 to 1 decimal place, if you first round to 2 decimal places you will get 4.65 which is 4.7 rounded to 1 decimal place. This is incorrect. The correct answer is 4.6

## Rounding Decimals Worksheets

The printable worksheets below provide questions for practice with rounding decimals.

There is also a rounding decimals worksheet generator that provides a limitless number of questions.