IGCSEMathsCambridge (CIE)CoreRevision NotesNumberOperations with Numbers & DecimalsOperations with Decimals

Operations with Decimals (Cambridge (CIE) IGCSE Maths: Core): Revision Note

Exam code: 0580 & 0980

Written by: Jamie Wood

Reviewed by: Dan Finlay

Updated on 25 November 2025

Operations with decimals

How do I add or subtract decimals without a calculator?

If the numbers involve decimals, the column methods for addition and subtraction can be used
- Line the place value columns up carefully
- Make sure the decimal points are all in the same column
  - Writing zeros (often called place value holders) can help keep everything in line
- e.g. 2.145 + 13.02 would be written as $02.145 + 13.020 .$

Worked Example

Johnny has £32.50 and spends £1.74.

Calculate how much money Johnny has left.

Answer:

This is a subtraction question as Johnny has spent money

Make a quick estimate

33 - 2 = 31

Align the digits by place value, ensuring £32.50 is the top number and using the decimal points as a starting point
Using place value holding zeros is optional

$32.50 - 01.74 .$

The column furthest right is the hundredths column
0 is smaller than 4 so borrow from the next (tenths) column

$4 32 . 5^{1} 0 - 01.74 . 6$

Next is the tenths column, but again 4 is smaller than 7 so borrow 10 from the ones column

$1 {}^{1}4 32 . 5^{1} 0 - 01.74 . 6$

14 - 7 = 7 in the tenths column and continue working 'right to left'

$1 {}^{1}4 32 . 5^{1} 0 - 01.74 30.76$

Check the final answer is similar to the estimate
£31 and £30.76 are reasonably close

Johnny has £30.76 left

How do I multiply decimals without a calculator?

The standard methods for multiplication can be easily adapted for use with decimal numbers
- E.g. column method, lattice method and grid method
You can make a problem easier by converting to integer values then undoing the action to the answer
- Multiply each value by a power of 10 to make it an integer
- Perform the easier multiplication
- Undo the initial action by dividing by the same powers of 10
- E.g. 2.5 x 4.01
  - Multiply 2.5 by 10 to give 25 and 4.01 by 100 to give 401
  - 25 x 401 = 10 025
  - Divide the answer by 10 and 100 to undo the initial changes
  - So the answer is 10.025
An alternative method is to ignore the decimal point whilst multiplying
- then put it back in the correct place for the final answer using estimation
- E.g. 1.3 × 2.3
  - Ignoring the decimals this is 13 × 23, which works out to 299
  - 1.3 × 2.3 is approximately 1.5 × 2, which is 3
  - So we know the answer should be close to 3, rather than 0.3 or 30
  - So the answer is 2.99

Examiner Tips and Tricks

A good way to check your answer without a calculator is to estimate it by rounding everything to 1 or 2 significant figures.

Worked Example

Without using a calculator, find 1.57 × 0.78 .

Answer:

Method 1

Multiply both values by powers of 10 to create a calculation using integer values

1.57 x 100 = 157
0.78 x 100 = 78

157 x 78

Using the grid method

	100	50	7
70	7000	3500	490
8	800	400	56

$7000 + 3500 49080040056 12246$

157 × 78 = 12 246

Undo the initial action by dividing the answer by 10 000
(This is dividing by 100 and then 100 again)

12 246 ÷ 10 000

1.2246

Method 2

Ignore decimal point to form a different, non-decimal calculation

157 × 78

Using the grid method

	100	50	7
70	7000	3500	490
8	800	400	56

$7000 + 3500 49080040056 12246$

157 × 78 = 12 246

Estimate the original calculation to write this as the correct answer

1.57 × 0.78 is approximately 2 × 1 = 2

So the correct answer is between 1 and 10

1.2246

How do I divide a decimal without a calculator?

Use a similar approach to when multiplying decimals
Make a problem easier by converting to integer values then undoing the action to the answer
- Write the division as a fraction
- Multiply each value by a power of 10 to make it an integer
- Perform the easier division
- Undo the initial action
  - divide by the same power of 10 the numerator was multiplied by
  - multiply by the same power of 10 the denominator was multiplied by
- E.g. 37.5 ÷ 0.25
  - $37.5 \div 0.25 \to \frac{37.5}{0.25}$
  - $\frac{37.5 \times 10}{0.25 \times 100} = \frac{375}{25}$
  - $\frac{375}{25} = 15$
  - Undo the initial actions $\frac{15 \times 100}{10}$
  - So the answer is 150
Alternatively, ignore the decimal point whilst carrying out the division
- then put it back in the correct place for the final answer using estimation
- E.g. 4.68 ÷ 6
  - 4.68 ÷ 6 is approximately 5 ÷ 6, which is between 1 and 0.5
  - So we know the answer should be 0.78, rather than 7.8 or 0.078

Worked Example

Without using a calculator, find 69.02 ÷ 0.7 .

Answer:

Method 1

Write as a fraction

$\frac{69.02}{0.7}$

Multiply both numbers by powers of 10 to create a calculation with integer values

$\frac{69.02 \times 100}{0.7 \times 10} = \frac{6902}{7}$

Use short division (bus stop method)

$70986 6^{6} 9^{6} 0^{4} 2$

$\frac{6902}{7} = 986$

Convert the answer
Divide by 100 to cancel out 69.02 being multiplied by 100
Multiply by 10 to cancel out 0.7 being multiplied by 10

$\frac{986 \times 10}{100}$

98.6

Method 2

Ignore the decimal point to form a different, non-decimal calculation

6902 ÷ 7

Use short division (bus stop method)

$70986 6^{6} 9^{6} 0^{4} 2$

6902 ÷ 7 = 986

Estimate the original calculation to write this as the correct answer

69.02 ÷ 0.7 is approximately 70 ÷ 1 = 70

So the correct answer is between 10 and 100

98.6

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Operations with Decimals (Cambridge (CIE) IGCSE Maths: Core): Revision Note

Operations with decimals

How do I add or subtract decimals without a calculator?

Worked Example

How do I multiply decimals without a calculator?

Examiner Tips and Tricks

Worked Example

How do I divide a decimal without a calculator?

Worked Example

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Jamie Wood

Reviewer: Dan Finlay