Decimals and Fractions 2
Multiplying and Dividing With Decimals

When multiplying or dividing by 10, 100, 1000, etc. the decimal point can simply be moved to the left or the right, although it should be noted that it is really the digits that are moving rather than the decimal point. When numbers such as 20, 200 or 300 are involved, the numbers can be multiplied by 2 or 3 and then the decimal point can be moved the correct number of places.

Worked Examples

1

Find.

(a)

362 × 100

Show me To multiply by 100 move the decimal point 2 places to the right.
To do this it is necessary to add two zeros to the number. So
362 × 100 = 362.00 × 100
= 36 200
(b)

4.73 × 10

Show me To multiply by 10, move the decimal point one place to the right. So

4.73 × 10 = 47.3
(c)

576 ÷ 10

Show me To divide by 10, move the decimal point one place to the left. So

576 ÷ 10 = 57.6
(d)

4.2 ÷ 1000

Show me To divide by 1000 move the decimal point three places to the left. To do this it is necessary to put some extra zeros in front of the number.

4.2 ÷ 1000 = 0.0042
2

Find.

(a)

3.4 × 20

Show me First multiply the 3.4 by 2 to give 6.8. Then multiply the 6.8 by 10 to give 68; so
3.4 × 20 = 3.4 × 2 × 10
= 6.8 × 10
= 68
(b)

Show me First divide 14.8 by 2 to give 7.4. Then divide by 10 to give 0.74.
=
= 0.74
(c)

Show me First multiply both numbers by 10 so that the 0.7 becomes a 7. This will make the calculation easier. Then divide 420 by 7 to give 60.
=
= 60

Exercises

Find.

(a)
4.74 × 10
(b)
6.32 × 100
(c)
41.6 ÷ 10
(d)
12.74 × 100
(e)
16.58 ÷ 100
(f)
32.4 ÷ 10
(g)
6.3 × 100
(h)
4.7 × 1000
(i)
3.2 × 10 000
(j)
47 × 1000
(k)
6.8 ÷ 1000
(l)
82 ÷ 100
(m)
192 ÷ 1000
(n)
14 ÷ 1000
(o)
0.18 × 1000

Find.

(a)
1.8 × 20
(b)
4.7 × 300
(c)
15 × 700
(d)
66 × 2000
(e)
15 × 400
(f)
1.3 × 8000
(g)
66 ÷ 20
(h)
74 ÷ 200
(i)
21 ÷ 3000
(j)
35 ÷ 5000
(k)
3.42 ÷ 20
(l)
52 ÷ 400
(m)
18.1 × 600
(n)
47.2 × 500
(o)
4.95 ÷ 50
(p)
3 × 0.02
(q)
15 × 0.04
(r)
5 × 0.000 7

Find.

(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)

The production cost for one chocolate bar is 5.27 pence.

(a)

What is the cost of producing:

(i)
4000 £
(ii)
17 000 £
(iii)
30 000 chocolate bars? £
(b)

A consultant says that he can reduce the production costs by 0.4 euro cents per bar. How much would this save on the production of:

(i)
5000 £
(ii)
22 000 £
(iii)
30 000 chocolate bars? £

For a major sporting event, a stadium is expected to hold its limit of 70 000 spectators.

(a)

How much money is taken in ticket sales if the price of the tickets were:

(i)
£5£
(ii)
£8£
(iii)
£11?£
(b)

If £432 000 is taken in ticket sales when the ticket price is £6 , how many spectators will not be able to get into the ground?

Using a calculator, or otherwise determine the value of 3.48 + and write the answer

(a)
exactly
(b)
correct to one decimal place
(c)
correct to one significant figure.

Information

The sides of the Great Pyramid of Giza in Egypt are about 230.5 m long. Although it was built thousands of years ago by thousands of slaves, the lengths of its sides vary by no more than 11.5 cm!

Challenge!

Without moving 6 adjacent numbers of the face of a clock, rearrange the other six so that the sum of every pair of adjacent numbers is a prime number.