## What does Rounding to the Nearest Hundred Mean?

**Rounding a number to the nearest hundred means to write down the multiple of 100 that is nearest to the number. If the nearest multiple of 100 is larger than the number, then we say that we round up. If the nearest multiple of 100 is smaller than the number, then we say that we round down.**

It is useful to round a number to the nearest hundred when estimating numbers. Sometimes it is easier to say that there were ‘about 200 people in a room’ instead of actually counting them all.

For example, we have the number 30 below.

It is nearer to zero than it is to 100.

This means that 30 rounds down to zero when rounded to the nearest hundred.

Here is the number 60.

We can see that 60 is closer to 100 than it is to zero.

This time, 60 rounds up to 100 instead of 0.

Here we have 50.

50 is directly in between 0 and 100. It is not nearer to 0 or 100 because it is exactly in between them both.

We have to decide whether to round 50 up or down.

We decide to round 50 up to 100 because we can make a rule for rounding.

51, 52, 53, 54, 55, 56, 57, 58 and 59 are all nearer to 100 than they are to 0.

If also round 50 up then we can say that if the tens digit is 5 or more, then we round up.

Even if we have a number like 50.1, it is nearer to 100 than it is to 0. If there is any other number added to 50, it is nearer to 100 and so, it is easiest to say that 50 rounds up.

The rule for rounding to the nearest hundred is to look at the tens digit.

If it is 5 or more, then round up.

If it is 4 or less, then round down.

Basically,in each hundred, all numbers up to 49 round down and numbers from 50 to 99 round up to the next hundred.

We normally use this rule to help us round numbers rather than drawing a number line.

Here we have 52.

The digit in the tens column of 52 is 5. 52 has 5 tens in it.

5 is ‘5 or more’ and so we round it up.

When first teaching rounding to the nearest hundred it is important to explain that we are actually writing down the nearest number in the 100 times table to the number we have.
Number lines can be a useful way to introduce the concept of rounding as it allows us to see the size of each number and where it is in relation with other numbers.

Once this concept is understood, it is recommended to just look at the tens digit to decide on how to round.

## How to Round to the Nearest Hundred

**To round to the nearest hundred:
**

**
**

**Look at the tens digit of the number.****
**- If it is 5 or more, round up.
- If it is 4 or less, round down.

**
**
To round up, increase the hundreds digit by 1 and set the tens and ones digits in the number to 0.

**
To round down, keep the hundreds digit the same and set the tens and ones digits in the number to 0.**

Here is an example in which we will round 379 to the nearest hundred.

The first step is to look at the tens digit, which is 7.

7 is ‘5 or more’ and so we round 379 up.

To round 379 number up, we increase the hundreds digit by 1 and set the other digits to zero.

We increase the 3 to a 4 and change the 7 and 9 to a zero.

379 rounded to the nearest hundred is 400.

This means that 379 is closer to 400 than it is to 300. This is because 379 is larger than 350, which is the halfway point between 300 and 400.

Here is another example of rounding to the nearest hundred.

We will round 628 to the nearest hundred.

The first step is to look at the tens digit, which is 2.

2 is ‘4 or less’ and so we round 628 down.

To round down, we keep the hundreds digit the same but change the other digits to zero.

The 6 in the hundreds column remains the same but the 2 and the 8 are set to zero.

628 rounds down to 600 when rounded to the nearest hundred.

In this example of rounding to the nearest hundred we look at 849.

The hundreds digit is 8 and so, the choice is to keep 8 as 8, or round it up to a 9. 849 is in between 800 and 900.

We first look at the tens digit, which is 4.

4 is ‘4 or less’ and so we round down.

We keep the 8 as an 8 and then set the remaining digits to zero.

849 rounds down to 800 when rounded to the nearest hundred.

**When teaching rounding to the nearest hundred, it is important to follow the simple process of looking at the tens digit only to decide whether to round up or down.
**

**
We do not look at any other digits beyond the tens digit to decide how to round to the nearest hundred.**

In the example of 849, we only look at the digit of 4. This tells us to round down.

A common mistake is to look beyond the 4. Some people will look at the 9 and round the 4 up to become a 5. They will then use this 5 to round up to 900.

This of course, is the wrong answer and we cannot use other digits to decide on rounding.

We can see from the number line that 849 is nearer to 800 than 900, so it must round down to 800. 849 is on the left of 850, which is the halfway mark.

## Rounding to the Nearest Hundred on a Number Line

**To round to the nearest hundred on a number line, write the number to be rounded between the multiples of 100 that are either side of it. Then mark halfway between the multiples of 100, where the last two digits are 50. If the original number is to the left of 50, round down and if it is to the right of 50, round up.**

50 is halfway between 0 and 100. The halfway point between each hundred is marked by a 50.

For example, round 3161 to the nearest hundred.

Even though we have thousands in this number, we still follow the same steps as before.

We look at the tens digit, which is 6.

6 rounds 3161 up to the next hundred because 6 is ‘5 or more’.

We currently have a 1 in the hundreds column. To round up, this 1 increases to a 2 and the digits after this are set to zero.

3161 rounds up to 3200.

We previously has 31 hundreds and now we have 32 hundreds.

This means that 3161 is nearer to 3200 than it is to 3100.

Here is an example of rounding 4982 to the nearest hundred.

Rounding to the nearest hundred means that we write down the nearest multiple of 100 to our number.

We have 49 hundreds in 4982. This means that we decide between rounding to 49 hundreds and 50 hundreds.

4982 is in between 4900 and 5000.

We look at the tens digit, which is 8.

8 is ‘5 or more’ and so, we round up.

We increase 49 hundreds to 50 hundreds.

4982 rounds up to 5000. This means that 4982 is nearer to 5000 than it is to 4900.

4982 is larger than 4950. 4950 is halfway between 4900 and 5000.

## Examples of Rounding to the Nearest Hundred

**Here are some examples of rounding to the nearest hundred:
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**

Example |
Tens Digit / Rounding |
Rounded to the Nearest Hundred |

234 |
3 is less than 5, so round down |
200 |

289 |
8 is 5 or more, so round up |
300 |

250 |
5 is 5 or more, so round up |
300 |

34 |
3 is less than 5, so round down |
0 |

72 |
7 is 5 or more, so round up |
100 |

1462 |
6 is 5 or more, so round up |
1500 |

5914 |
1 is less than 5, so round down |
5900 |

6987 |
9 is 5 or more, so round up |
7000 |