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.
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 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."
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.
|7.8 rounded to the nearest whole unit is 8|
7.8 is between the whole units 7 and 8.
|.33 rounded to the nearest tenth|
.33 is between 3 and 4 tenths (.3 and .4).
|.462 rounded to the nearest hundredth|
.462 is between 46 and 47 hundredths (.46 and .47).
You can round decimals without the help of a number line using the steps as shown in the example below
|Round 2.719 to the nearest tenth|
The place to the right of the tenths has the digit 1. We round down which means the digit in the tenth place stays the same.
2.719 rounded to the nearest tenth is 2.7
The examples below show how the steps above can be applied when rounding to the nearest whole number, nearest tenth, and nearest hundredth.
|Steps||Ex. 1||Ex. 2||Ex. 3|
|Let’s round a number to the nearest whole number||8.9||3.4||24.7|
|Find the tenths' place.||8.9||3.4||24.7|
|If it is less than 5, round the whole number down (it stays the same).||3|
|If it is 5 or more, round the whole number up.||9||25|
|Steps||Ex. 1||Ex. 2||Ex. 3|
|Round a number to the nearest tenth||3.14||.883||6.26|
|Find the hundredths' place.||3.14||.883||6.26|
|Less than 5, round the tenth down.||3.1|
|If it is 5 or more, round the tenth up.||.9||6.3|
|Steps||Ex. 1||Ex. 2||Ex.3|
|Round a number to the nearest hundredth||6.173||1.019||.955|
|Find the thousandths' place.||6.173||1.019||.955|
|Less than 5, round the hundredth down (it stays the same).||6.17|
|If it is 5 or more, round the hundredth up.||1.02||.96|
You can use the Rounding Calculator below to check your answers and also to try some more examples for yourself.
Problems like the example below can sometimes be a little trickier. They require a good understanding of decimal place value.
|Round 9.999 to the nearest hundredth.|
|Find the thousandths' place.||9.999|
|Less than 5, round the hundredth down (it stays the same).|
|If it is 5 or more, round the hundredth up. This means we have 10 hundredths. We must exchange these for 1 tenth which means we have 10 tenths. Again we must exchange these for 1 whole unit which adds to the 9 to make 10.||10.00|
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
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.