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In order to access this I need to be confident with:

Place value

Multiples

This topic is relevant for:

Here we will learn about **rounding numbers to the** **nearest 10, 100, and 1000**.

There are also rounding worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Rounding to the nearest ** allows us to approximate the size of a number.

We need to identify the number to the **right** of the tens, hundreds or thousands column depending on what we are rounding to.

If this number** less than**

If this number is

E.g.

Round

The number to the right of the tens column is

So **120**.

E.g.

Round

The number to the right of the hundreds column is

So** 500**.

E.g.

Round

The number to the right of the thousands column is

So** 3000**.

Let’s quickly recap place value by looking at the

It can be split into

Thousands | Hundreds | Tens | Ones | Tenths |

1 | 2 | 4 | 5 | 0 |

Using a place value chart can help us to identify the place value of the digits when we are rounding to the nearest

In order to round to the nearest

- Check if the number is a multiple of
10 , if it is, do nothing. - If the ones digit is less than
5 , round down to the previous10 . - If the ones digit is
5 or more than5 , round up to the next10 .

Get your free rounding to the nearest 10, 100 and 1000 worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONGet your free rounding to the nearest 10, 100 and 1000 worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONRound

**Check the number is already a multiple of**10 , if it is, do nothing.

2**If the ones digit is less than 5, round down to the previous 10**.

The digit to the right of the tens digit is the ones digit which is

This means that we round down to the previous

This means that the tens digit will stay the same and the ones digit will become

So ** 20**.

Round

**Check if the number is a multiple of 10, if it is, do nothing.**

**If the ones digit is 5 or more than 5, round up to the next 10**

The ones digit (the digit to the right of the tens digit) is

This means that we round up to the next

We need to add

Therefore the

So ** 70**.

In order to round to the nearest

**Check if the number is a multiple of**100 , if it is, do nothing.**If the tens digit is less than**5 , round down to the previous100 .**If the tens digit is**5 or more than5 , round up to the next100 .

What is

**Check if the number is a multiple of 100, if it is, do nothing.**

**If the tens digit is 5 or more than 5, round up to the next 100.**

The tens digit (the digit to the right of the hundreds digit) is

This means that we round up to the next

We need to add

So ** 500**.

What is

**Check if the number is a multiple of 100, if it is, do nothing.**

350 is a multiple of 10 but not a multiple of 100, so we will move on to step 2.

** If the tens digit is**

The tens digit (the digit to the right of the hundreds digit) is

This means that we round up to the next

We need to add

Therefore the

So ** 400**.

In order to round to the nearest

**Check if the number is a multiple of**1000 , if it is, do nothing.**If the hundreds digit is less than**5 , round down to the previous1000 .**If the hundreds digit is**5 or more than5 , round up to the next1000 .

Round

**Check if the number is a multiple of 1000, if it is, do nothing.**

**If the hundreds digit is less than 5, round down to the previous 1000.**

The hundreds digit (the digit to the right of the thousands digit) is

This means that we round down to the previous

This means that the thousands digit will stay the same and the hundreds, tens and ones digits will become zeros.

So ** 2000**.

There are

**Check if the number is a multiple of 1000, if it is, do nothing.**

**If the hundreds digit is 5 or more than 5, round up to the next 1000**.

The hundreds digit is

So ** 5000**.

**The number**5

Most mistakes occur when dealing with the number

On a number line it is in the middle so it is easier to think you can go in either direction however **you must round up.**

E.g.

15 rounded to the nearest10 is20 .857 rounded to the nearest100 is900 .3520 rounded to the nearest1000 is4000 .

**Which digit to look at**

When rounding to the nearest

E.g.

Round

With this question we need to look at the **tens digit.**

In this example the tens digit is

Rounding to the nearest 10, 100 and 1000 is part of our series of lessons to support revision on rounding numbers. You may find it helpful to start with the main rounding numbers lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Round 212.65 to the nearest 10.

210

10

200

212.7

The ones digit is 2 , which is less than 5 , so we round down to the previous 10 . Therefore the answer is 210 .

There are 563 spectators at a snooker match. Josh states ‘There were approximately 600 people there.’ Phil states ‘There were about 500 people there. Who has correctly rounded to the nearest 100 ?

Phil

Josh

Neither of them

Either could be correct

The tens digit is 6 , which is greater than 5 , so we round up to the next 100 . The answer is 600 .

3. Round 1236 to the nearest hundred.

1000

200

1300

1200

The tens digit is 3 , which is less than 5 , so we round down to the previous 100 . The answer is 1200 .

4. During a football match between Manchester United and Watford FC there were 16,543 fans in attendance. What is this number rounded to the nearest thousand?

20,000

10,000

16,000

17,000

The hundreds digit is 5 so we round up to the next thousand so the answer is 17,000 .

5. The mileage on a car is showing 56,734 miles. What is this number rounded to the nearest thousand?

60,000

50,000

57,000

56,000

The hundreds digit is 7 , which is greater than 5 , so we round up to the next 1000 . Therefore the answer is 57,000 .

6. A florist sells 60 bouquets rounded to the nearest 10 on Saturday. What is the maximum number of bouquets she could have sold?

60

69

64

55

The number of bouquets needs to round down to 60 (to the nearest 10 ). We know that numbers with a 5 and above round up and numbers below 5 round down.

The numbers that will round down to 60 are 61, 62, 63 and 64 .

So the biggest number that will round down to 60 is 64 .

1.(a) Write the number thirty thousand, three hundred and seven in figures.

(b) Round this number to the nearest 10 .

**(2 marks)**

Show answer

a) 30, 307

**(1)**

b) 30, 310

**(1)**

2. (a) What is the value of 636,213 rounded to the nearest thousand?

(b) If I instead rounded to the nearest hundred, what would be the difference in my two answers.

**(3 marks)**

Show answer

a) 636,000

**(1)**

b) 636,200

(rounding to the nearest hundred)

**(1)**

636,200 – 636,000 = 200

(correct subtraction)

**(1)**

3. Tim thinks of a number and rounds it to the nearest 10 . His number is 50 .

(a) What is the smallest possible whole number he could have thought of?

(b) What is the largest possible whole number he could have thought of?

**(2 marks)**

Show answer

a) 45

**(1)**

b) 54

**(1)**

You have now learned how to:

- Round numbers to the nearest 10, 100 and 1000.

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