Basic Engineering Mathematics, Fifth Edition

Percentages 35

10. Express as percentages, correct to 3 significant
    figures,

(a)

7

33

(b)

19

24

(c) 1

11

16

11. Place the followingin order of size, the small-
    est first, expressing each as a percentage
    correct to 1 decimal place.

(a)

12

21

(b)

9

17

(c)

5

9

(d)

6

11

12. Express 65% as a fraction in its simplest form.


13. Express 31.25% as a fraction in its simplest
    form.


14. Express 56.25% as a fraction in its simplest
    form.


15. Evaluate A to J in the following table.

Decimal number Fraction Percentage

0.5 A B

C

1

4

D

E F 30

G

3

5

H

I J 85

5.3 Further percentage calculations

5.3.1 Finding a percentage of a quantity

Tofindapercentageofaquantity,convertthepercentage
to a fraction (by dividing by100) andremember that ‘of’
means multiply.

Problem 10. Find 27% of £65

27% of £65=

27

100

× 65

=£17.55by calculator

Problem 11. In a machine shop, it takes 32

minutes to machine a certain part. Using a new tool,

the time can be reduced by 12.5%. Calculate the

new time taken

12.5% of 32 minutes=

12. 5

100

× 32

=4 minutes

Hence,new time taken= 32 − 4 =28 minutes.

Alternatively, if the time is reduced by 12.5%, it now

takes 100%− 12 .5%= 87 .5% of the original time, i.e.

87 .5% of 32 minutes=

87. 5

100

× 32

=28 minutes

Problem 12. A 160 GB iPod is advertised as

costing £190 excluding VAT. If VAT is added at

17.5%, what will be the total cost of the iPod?

VAT= 17 .5% of £190=

17. 5

100

× 190 =£33. 25

Total cost of iPod=£190+£33. 25 =£223.25

A quicker method to determine the total cost is: 1. 175 ×

£190=£223.25

5.3.2 Expressing one quantity as a

percentage of another quantity

To express onequantity as apercentageof another quan-

tity,dividethe first quantity by the second then multiply

by 100.

Problem 13. Express 23cm as a percentage of

72cm, correct to the nearest 1%

23cm as a percentage of 72cm=

23

72

×100%

= 31. 94444 ...%

=32%correct to

the nearest 1%

Problem 14. Express 47 minutes as a percentage

of 2 hours, correct to 1 decimal place

Note that it is essential that the two quantities are in the

same units.

Working in minute units, 2 hours= 2 × 60

=120 minutes

47 minutes as a percentage

of 120 min=

47

120

×100%

=39.2%correct to

1 decimal place