What is rounding?
Rounding is a very useful tool in maths. It means you replace a numerical value with another that is approximately the same but simplier to use.
It is used to obtain a value that is easier to use; either to write down or to handle in the maths you are working on.
It does however, introduce errors into a calculation. If you are aware of this, then it is fine and can be a very useful tool for any mathmatician.
Why do we use rounding?
Rounding is used all the time to make life easier. It gives you a rough idea what the answer should be, an estimate that is easy to work out.
A real life example of using rounding is when people go shopping. A lot of people use the strategy of rounding to quickly get an idea of how much they have spent. Instead of adding £3.99 and £2.99, it is easy to round them both and add £4 and £3 so you know how much to give to the shop keeper.
When working with maths all the time, rounding is used to estimate the answer to a problem and then once you do it properly you already know where the answer should be around.
What do you need to know first before anything else?
Place value. Its that simple, without having a secure knowledge of place value then you will find rounding hard.
You will be able to round any number up to and including the value of the digit you know. So for example, if you know where the hundreds column is, then you can round to the nearest hundred. If you know where the thousandths column is, then you can round to the nearest thousandths.
How do I round to the nearest 10?
This is the simpliest form of rounding. It is what you are taught first in schools but the basics behind this is what you use for any rounding you will meet after.
Using a number line helps you to see how rounding works. To do this we plot the number on the number line. We then have a look to find the nearest multiple of 10, (i.e. if we had a number of 14, the multiples of 10 we look at are 10 and 20 because a multiple of 10 has to have a 0 in the units column.) We count to see how close it is to both multiples of 10. The smallest or closest is the number we round to.
If we went back to the number 14, then it is 4 away from 10 and 6 away from 20. So if we rounded 14 to the nearest 10 then we round it to 10.
The only number which doesn't make sense here is when the units column has a 5 in it, because it will be 5 away from each multiple of 10. In this case we all agree that we should round up to the bigger multiple of 10, (15 would round up to 20, 35, would round up to 40 and 145 would round up to 150.)
And this is where you first come across the rule that you use for every rounding exercise you will come across. 1-4 you round down and 5 or more you round up.
NOTE: If you are rounding down then leave the 10's column the same and put a 0 in the units column. If you are rounding up then you add a 1 to the 10's column and put a 0 in the units column.
Example 1 ( round 78 to the nearest 10)
Once plotted on a number line you can see that it is closer to 80 than 70. Plus we know that the units column is an 8, which is greater than 5, so we needed to round it up.
Example 2 (162 to the nearest 10)
Again, once plotted on a number line you can see that it is closer to 160 than 170. And we know that the units column is a 2, which is between 1-4, so we needed to round down.
How to round to the nearest 100.
Rounding to the nearest 100 is a little harder than rounding to the nearest 10 but you use exactly the same method as rounding to the nearest 10.
The first thing you need to know is which number is the 100's column. Once you have found this you need to look to the right at the 10's column. If this digit is 1-4 you round down, if it is 5 or more then you round up.
Again, if you are rounding down, then you leave the 100's column the same and every digit to the right you put a 0 in its place (a multiple of a 100, has to have a 0 in the tens column and the units column.)
If you are rounding up then you add one to the 100's column and every digit to the right you put a 0 in its place.
Example 3 (158 to the nearest 100)
Using the number line, it is 42 away from 200, but 58 away from 100. So rounding it to the nearest 100 is 200.
Using the maths:
Find the 100's column first which is the digit 1. Then look to the column to the right (10's column) If this is 1-4 then we round down, 5 or more we round up. In the 10's column we have a 5, so we round up. If we round up then we add 1 to the hundreds column and then put 0's in the other columns to the right, which makes 200.
Rounding to the nearest 1000
Rounding to the nearest 1000 is a little harder still but you still use the same method as rounding to the nearest 10.
The first thing you do is look for the 1000's column. Once you have found this you need to look to the right at the 100's column. If the digit here is 1-4 you round down, if it is 5 or more you round up.
If you are rounding down then you leave the 1000's column the same and every number to the right you put a 0 to mark its place, (a multiple of 1000 has to have a 0 in the hundreds, tens and units columns.)
If you are rounding up then you add one to the 1000's column and every number to the right you put a 0 to mark its place.
Example 4 (round 5479 to the nearest 1000)
If placed on a number line you can see that it is 479 away from 5000 but 581 away from 6000. So 5479 rounded to the nearest 1000 is 5000.
Using the maths:
Find the 1000's column. The digit 5 is in the 1000's column. Then look to the column to the right (100's column) If this is 1-4 then you round down, if it is 5 or more then you round up.
In this case the digit 4 is in the column to the right so we round down. If we are rounding down we leave the 1000's column as it is and put 0's in the place of the other digits to the right. In this case we leave the 5 thousands as they are and put 0's in the other columns making 5000.
Rounding can become harder when you deal with bigger or even very small numbers (decimals). So a tip you can use to make it easier for yourself is to only look at the two digits you need to concentrate on; the place value column you are looking for and the digit to the right of this.
Once you find these two digits just treat them like you were rounding to the nearest 10. Any digit to the left of this needs to be left alone and just re-written. Any digit to the right of the place value column you are looking for will have a 0 in its place.
Example 5 (46225 rounded to the nearest 1000)
So we need to find the 1000's column. The digit 6 is in the 1000's column. We then look to the column to the right, which is the 100's column in this example. We find the digit 2 in this column.
So we are looking at the two most important digits in this example, which are 62 and treat it like we are rounding to the nearest 10. 62 to the nearest 10 is 60.
Every digit to the left of this needs to stop the same (so the 4 in the ten-thousand column needs to stay the same) Then we can write the 6 and 0 in the next couple of columns. The rest need to be filled with 0's.
So we write 46000. 46225 to the nearest 1000 is 46000.
A great website to practice rounding
- Dartboard - Rounding - 6-12 year olds - Topmarks
Use an image of a dartboard to reinforce rounding skills to the nearest 10, 100, 1000 or whole number when using decimals. Choose to reveal the answers or input your own. Round pounds, metres and Kg too.
The rounding rap
The rounding rap is a great video/song that will help you remember how to round to the nearest 10,100 or 1000.
If you are confident with place value then you can round any number.
Take a look at the video below and see how similar the method is to round 10,100 or 1000.