GCSE Maths Number Rounding Numbers

Rounding To The Nearest 10, 100, 1000

# Rounding to the Nearest 10, 100 and 1000

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.

## What is rounding to 10, 100 and 1000

Rounding to the nearest 10, 100, and 1000 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 5, round down.
If this number is 5 or more than 5, round up.

E.g.
Round 123 to the nearest 10.

The number to the right of the tens column is 3 which is less than 5 so we round down.
So 123 rounded to the nearest 123 is 120.

E.g.
Round 475 to the nearest 100.

The number to the right of the hundreds column is 7 which is more than 5 so we round up.
So 475 rounded to the nearest 100 is 500.

E.g.
Round 2517 to the nearest 1000.

The number to the right of the thousands column is 5 so we round up.
So 2517 rounded to the nearest 1000 is 3000.

Let’s quickly recap place value by looking at the 4 digit number:

1245

It can be split into 1 thousand, 2 hundreds, 4 tens and 5 ones by placing the digits onto a place value chart.

Using a place value chart can help us to identify the place value of the digits when we are rounding to the nearest 10, 100 and 1000.

## How to round numbers to the nearest 10

In order to round to the nearest 10:

1. Check if the number is a multiple of 10, if it is, do nothing.
2. If the ones digit is less than 5, round down to the previous 10.
3. If the ones digit is 5 or more than 5, round up to the next 10.

## Rounding to 10 examples

### Example 1: rounding numbers to the nearest 10

Round 23 to the nearest 10.

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

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

2If 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 3 which is less than 5.
This means that we round down to the previous 10.

This means that the tens digit will stay the same and the ones digit will become 0.

So 23 rounded to the nearest ten is 20.

### Example 2: rounding numbers to the nearest 10

Round 67 to the nearest 10.

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

### How to round numbers to the nearest 100

In order to round to the nearest 100:

1. Check if the number is a multiple of 100, if it is, do nothing.
2. If the tens digit is less than 5, round down to the previous 100.
3. If the tens digit is 5 or more than 5, round up to the next 100.

## Rounding to 100 examples

### Example 3: rounding numbers to the nearest 100

What is 478 to the nearest 100?

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.

### Example 4: rounding numbers to the nearest 100

What is 350 rounded to the nearest 100?

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.

### How to round numbers to the nearest 1000

In order to round to the nearest 1000:

1. Check if the number is a multiple of 1000, if it is, do nothing.
2. If the hundreds digit is less than 5, round down to the previous 1000.
3. If the hundreds digit is 5 or more than 5, round up to the next 1000.

## Rounding to 1000 examples

### Example 5: rounding numbers to the nearest 1000

Round 2346 to the nearest 1000.

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.

### Example 6: word problem

There are 4709 people watching a cricket match. Round this to the nearest thousand.

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.

### Common misconceptions

• The number 5

Most mistakes occur when dealing with the number 5.
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 nearest 10 is 20.
• 857 rounded to the nearest 100 is 900.
• 3520 rounded to the nearest 1000 is 4000.

• Which digit to look at

When rounding to the nearest 10, 100 or 1000 you must identify either the tens, hundreds or thousands digit and then use the digit to the right of it.

E.g.
Round 2545 to the nearest 100.

With this question we need to look at the tens digit.
In this example the tens digit is 4 so we round down to the previous 100.
2545 rounded to the nearest 100 is 2500.

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:

### Practice rounding to the nearest 10, 100 and 1000 questions

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 .

### Rounding to the nearest 10, 100 and 1000 GCSE questions

1.(a) Write the number thirty thousand, three hundred and seven in figures.
(b) Round this number to the nearest 10 .

(2 marks)

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)

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)

a) 45

(1)

b) 54

(1)

## Learning checklist

You have now learned how to:

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

## Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.