Unit 6 Section 3 : Multiplying with Decimals

In this section we will extend our multiplication to include decimals.

It helps to think of any number which includes a decimal part as a whole number which has been adjusted by dividing by 10, 100, 1000 etc.

For example:

3.5 = 35 ÷ 10 0.8 = 8 ÷ 10 4.25 = 425 ÷ 100

Try and work out how you would rewrite the following decimal numbers as whole numbers divided by 10, 100 or 1000. Once you think you know the answer to each one, click on the button marked to see whether you are correct.

(a)	4.7
(b)	0.3
(c)	54.3

Now we can think about questions which have decimal parts in a different way.
Look carefully at the examples below - each stage is explained in square brackets.

Example 1 :	3.5 × 19
	=	35 ÷ 10 × 19	[replace the 3.5 by 35 ÷ 10]
	=	35 × 19 ÷ 10	[we can ÷10 and ×19 in either order]
	=	665 ÷ 10	[35 × 19 = 665 using one of the methods in section 6.2]
	=	66.5

Example 2 :	9.2 × 0.8
	=	92 ÷ 10 × 8 ÷ 10	[replace 9.2 by 92 ÷ 10 and replace 0.8 by 8 ÷ 10]
	=	92 × 8 ÷ 10 ÷ 10	[we can ÷10 and ×8 in either order]
	=	736 ÷ 10 ÷ 10	[92 × 8 = 736 using one of the methods in section 6.2]
	=	7.36

Practice Question
Work out the answer to this question on paper and then click on to see whether you are correct.

What is 24 × 15.3?

Exercises

Question 1
Find the answers to the multiplications involving decimals below (but not using a calculator).

(a)	3 × 0.8
(b)	9 × 1.2
(c)	5 × 0.7
(d)	3 × 2.6
(e)	6 × 1.5
(f)	8 × 7.9
(g)	2.1 × 3.2
(h)	5.6 × 7.2
(i)	8.4 × 2.1
(j)	9.2 × 1.8
(k)	1.2 × 6.2
(l)	15 × 7.3
(m)	22 × 9.4
(n)	7.1 × 62
(o)	74 × 5.3