GCSE Maths Number

Rounding Numbers

# Rounding Numbers

Here we will learn about rounding including how to round a number to the nearest 10, 100 or 1000, how to round a number to a given number of decimal places and how to round a number to a given number of significant figures. We will also learn about truncation and how we can also use rounded numbers to estimate the solution to a calculation.

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?

Rounding is when we approximate numbers in order to make them easier to deal with. We need to round down or up depending on which value is nearer.

There are several ways we can be asked to round a number.

E.g.

1478.27 can be rounded in several ways

• Rounding to the nearest ones place, 10, 100 and 1000
1478.47 is 1478 rounded to the nearest ones place
1478.47 is 1480 rounded to the nearest 10
1478.47 is 1500 rounded to the nearest 100
1478.47 is 1000 rounded to the nearest 1000
• Rounding to significant figures
1478.47 is 1000 rounded to 1 significant figure
1478.47 is 1500 rounded to 2 significant figures
1478.47 is 1480 rounded to 3 significant figures
• Rounding to decimal places
1478.2735 is 1478.3 rounded to 1 decimal place (the nearest tenth)
1478.2735 is 1478.27 rounded to 2 decimal places (the nearest hundredth)
1478.2735 is 1478.274 rounded to 3 decimal places (the nearest thousandth)

Truncating a number and estimation are also linked with rounding:

• Truncation is cutting a number off at a certain value with no need to round up.
• Estimation is using the approximated numbers for a calculation; we do not use the exact numbers.

## How to round numbers

In order to round a number:

1. Identify the number to the right of the place value column you are rounding to
2. If it is a 4 or less we round down, if it is a 5 or more we round up
3. Write the answer.

## Rounding numbers examples

### Example 1: rounding to the nearest 10, 100 and 1000

Round 382 to the nearest 10.

1. Identify the number to the right of the place value column you are rounding to

We are rounding to the nearest 10 so we identify the number to the right of the 8 in the tens column.
This is a 2.

2 If it is a 4 or less we round down, if it is a 5 or more we round up

It is a 2 is 4 or less so we round down to 380.

3 Write the answer.

382 is 380 rounded to the nearest 10

Step-by-step guide: Rounding to the nearest 10, 100 and 1000

### Example 2: rounding to decimal places

Round 14.76 to 1 decimal place (to 1 dp).

Identify the number to the right of the place value column you are rounding to

If it is a 4 or less we round down, if it is a 5 or more we round up

Write the answer.

Step-by-step guide: Decimal places

### Example 3: rounding to decimal places

Round 25.673 to the nearest whole number.

Identify the number to the right of the place value column you are rounding to

If it is a 4 or less we round down, if it is a 5 or more we round up

Write the answer.

Step-by-step guide: Rounding decimals

### Example 4: rounding to significant figures

Round 357 to 1 significant figure.

Identify the number to the right of the place value column you are rounding to

If it is a 4 or less we round down, if it is a 5 or more we round up

Write the answer.

Step-by-step guide: Significant figures

### Example 5: rounding to significant figures

Round 7.5823 to 2 significant figures (to 2 sf).

Identify the number to the right of the place value column you are rounding to

If it is a 4 or less we round down, if it is a 5 or more we round up

Write the answer.

Step-by-step guide: Upper and lower bounds

See also: Place value

### Example 6: truncation

Truncate 94.5871 to 2 decimal places (to 2 dp).

Identify the number in the place value column you are truncating to

Round the number to what is asked for. Round down or up as required.

Write the answer.

Step-by-step guide: Truncation

See also: Error intervals

### Example 7: estimation

Estimate the following calculation:

287.1 × 14.7

Identify the number to the right of the place value column you are rounding to

If it is a 4 or less we round down, if it is a 5 or more we round up

Write the answer.

Step-by-step guide: Estimation

### Common misconceptions

• Remember to put zero in as a place holder before the decimal point

E.g.
When we round 2769.1 to the nearest 100 the answer will be 2700 because we need zeros as place holders in the tens and units columns.

2739.1 ≈ 2700

NOT 27

• Sometimes we need a zero in as a place holder with decimal numbers

E.g.
When we round 3.4973 to 2 decimal places the answer will be 3.50 because we need the zero in the hundredths column to show the two decimal places.

3.4973 ≈ 3.50

• Estimation of numbers within square roots

If your estimation involves a square root symbol, round those numbers to the nearest square number.

E.g.

$13.45 + \sqrt{23.6} \approx10 + \sqrt{25} = 10 +5 = 15$

### Rounding practice questions

1. Round 193 to the nearest 100 .

100

200

1

2

We are rounding to the nearest 100 . Identifying the 9 in the tens column indicates we need to round up.

2. Round 13.782 to 2 decimal places.

13.79

13.78

13.780

13.00

We are rounding to 2 decimal places. The 2 in the thousandths column indicates that we should round down.

3. Round 5692 to 2 significant figures.

5600

6000

5700

5690

We are rounding to 2 significant figures. The 9 in the tens column indicates we round up. We need to have zeros in the tens and ones columns as place holders.

4. Round 0.0365 to 2 significant figures.

0.03

0.3

0.036

0.037

We are rounding to 2 significant figures. The second significant figure is 6 .

The 5 in the ten thousandths column indicates we round the 6 up.

5.  Truncate 78 to the nearest 10 .

78

70

80

7

We locate the digit in the tens column and truncate to this degree of accuracy, replacing the digit in the ones column with a zero.

6.  Estimate   341 × 27 .

9207

9000

6800

9200

By first rounding each number to one significant figure, the calculation becomes

300\times30 = 9000

### Rounding GCSE Questions

1. Write 78 348 correct to the nearest 1000 .

(1 Mark)

Show answer

78 000

(1)

2. (a)  Write 8400 correct to one significant figure.

(b) Write 3.51 correct to one significant figure.

(2 Marks)

Show answer

(a)

8000

(1)

(b)

4

(1)

3. Work out an estimate for

\frac{572\times213}{36} .

(2 Marks)

Show answer

For rounding one original number to 1 significant figure 600 or 200 or 40

\frac{600\times200}{40}

(1)

For the calculation involving all three correctly rounded numbers.

(1)

for the correct answer

= 3000

(1)

4. (a)  Use your calculator to work out

\frac{65.4+49.3}{23.4-15.8}

Write down all the figures on your display.

(b)  Write your answer to part (a) to 1 decimal place.

(2 Marks)

Show answer

(a) 15.092105…

(1)

(b)   15.1 (1.d.p)

(1)

## Learning checklist

You have now learned how to:

• Round numbers to a number of decimal places
• Round numbers to a number of significant figures
• Use approximation through rounding to estimate answers

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