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Place value

DecimalsAddition and subtraction

Money

Multiplying and dividing by 10, 100, 1000,...

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Here we will learn about **multiplying decimals** including how to multiply decimals by a whole number and multiply decimals by decimals.

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

**Multiplying decimals** is where we multiply together decimal numbers.

To** **multiply decimals we first need to multiply by powers of ten to turn the decimals into whole numbers. We then need to divide by powers of ten at the end to get our final answer.

Multiplying decimals is important when dealing with money problems such as the conversion of currency. It is also a vital skill when converting between metric units and other multiplication problems.

E.g.

When solving problems where we need to multiply or divide decimals, we need to multiply and divide by powers of ten.

When we multiply by a power of ten, each digit increases in place value.

If we multiply by

E.g.

If we divide by

E.g.

To multiply decimals we will multiply by powers of ten at the start, and then divide by powers of ten at the end to get our final answer.

In order to multiply decimals:

**Multiply any decimal numbers by an appropriate power of ten to make them whole numbers.****Use column multiplication (or another preferred method) to find the product of the numbers.****Divide the product from Step 2 by the powers of ten used in Step 1. Check that the total number of decimal digits in the question is the same as the total number of decimal digits in the answer.**

Get your free Multiplying decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free Multiplying decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEWork out

**Multiply any decimal numbers by an appropriate power of ten to make them whole numbers**.

Multiply

2**Use column multiplication (or another preferred method) to find the product of the numbers**.

3**Divide the product from Step 2 by the powers of ten used in Step 1. Check that the total number of decimal digits in the question is the same as the total number of decimal digits in the answer**.

In Step 1 we multiplied

Check that the total number of decimal places in the question matches the total number of decimal places in the answer.

The answer is

Work out

**Multiply any decimal numbers by an appropriate power of ten to make them whole numbers.**

Multiply

**Use column multiplication (or another preferred method) to find the product of the numbers.**

**Divide the product from Step 2 by the powers of ten used in Step 1. Check that the total number of decimal digits in the question is the same as the total number of decimal digits in the answer.**

In Step 1 we multiplied

Check that the total number of decimal places in the question matches the total number of decimal places in the answer.

The trailing zero can now be removed.

The answer is

Work out

**Multiply any decimal numbers by an appropriate power of ten to make them whole numbers.**

Multiply

**Use column multiplication (or another preferred method) to find the product of the numbers.**

**Divide the product from Step 2 by the powers of ten used in Step 1. Check that the total number of decimal digits in the question is the same as the total number of decimal digits in the answer.**

In Step 1 we multiplied

1

Check that the total number of decimal places in the question matches the total number of decimal places in the answer.

The answer is

Work out

**Multiply any decimal numbers by an appropriate power of ten to make them whole numbers.**

Multiply

**Use column multiplication (or another preferred method) to find the product of the numbers.**

In Step 1 we multiplied

Check that the total number of decimals in the question matches the total number of decimals in the answer.

The answer is

**Decimal point in the wrong position in the answer**

It is very common for the answer to have the decimal point in the wrong position in the answer. It is important to remember what powers of ten were used at the start and reverse that for the final answer. Checking that the total number of decimals in the question is the same as the total number of decimals in the answer is a way to avoid this. Also rounding the numbers in the question to

E.g.

1. Multiply together 6 and 2.8

1.68

16.8

12.48

168

Work out 6\times28 and then divide the answer by 10

2. Work out 9.4\times16

150.4

1504

144.64

15.04

Work out 94\times16 and then divide the answer by 10

3. Work out 23\times0.17

391

39.1

23.161

3.91

Work out 23\times17 and then divide the answer by 100

4. Multiply together 5.6 and 9.8

5488

54.88

45.48

15.4

Work out 56\times98 and then divide the answer by 100

5. Find the product of 4.83 and 7.2

347.76

28.166

34.776

29.66

Work out 483\times72 and then divide the answer by 1000

6. Work out 2\times3.7\times1.54

11.396

11396

6.378

7.24

Work out 2\times37\times154 and then divide the answer by 1000

1. You are given that 132\times451 = 59532 . Use this information to work out the following:

(a) 13.2\times451

(b) 1.32\times4.51

(c) 13.2\times0.451

**(3 marks)**

Show answer

(a) 5953.2

**(1)**

(b) 5.9532

**(1)**

(c) 5.9532

**(1)**

2. (a) Find the cost of 12 bottles of sparkling water costing £1.69 each.

(b) At a cinema, adult tickets cost £7.75 and child tickets cost £5.49 . Find the total cost of 5 adults and 7 children

**(5 marks)**

Show answer

(a) 12 \times 169

**(1)**

£20.28 i

**(1)**

(b) 5 \times7.75 or 7\times5.49

**(1)**

38.75 or 38.43

**(1)**

Correct answer of £77.18

**(1)**

3. Calculate the area of the rectangle

**(2 marks)**

Show answer

12.4\times8.7 i

**(1)**

107.88 i

**(1)**

You have now learned how to:

- Understand and use place value for decimals, measures and integers of any size
- Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

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