Middle Years

# 4.02 Conversions

Worksheet
Percentages and fractions
1

State whether the following are the same as 80\%:

a

\dfrac{80}{10}

b

\dfrac{4}{5}

c

0.8

d

\dfrac{80}{100}\%

2

Express the following percentages as fractions with denominators of 100:

a
17\%
b
6\%
c
43\%
d
20\%
e
92\%
f
55\%
g
100\%
h
71\%
3

Express the following fractions as percentages:

a
\dfrac{1}{100}
b
\dfrac{40}{100}
c
\dfrac{13}{100}
d
\dfrac{69}{100}
e
\dfrac{100}{100}
f
\dfrac{73}{100}
g
\dfrac{120}{100}
h
\dfrac{58}{100}
4

Express the following percentages as simplified fractions:

a
8\%
b
35\%
c
4.5\%
d
15.8\%
e
49.03\%
f
0.02\%
g
0.1\%
5

Express the following fractions as percentages, rounding your answer to two decimal places when necessary:

a

\dfrac{13}{50}

b

\dfrac{11}{20}

c

\dfrac{48}{73}

d

\dfrac{39}{60}

Percentages and decimals
6

Convert the following percentages to decimals:

a
60\%
b
7\%
c
62\%
d
25\%
e
100\%
f
55\%
g
0.07\%
h
0.3\%
i
9.8\%
j
6.42\%
k
18.41\%
l

270\%

m
500\%
7

Convert the following decimals to percentages:

a
0.75
b
0.13
c
0.51
d
1
e
0.9
f
0.4
g
0.051
h
0.009
i
0.077
j
0.274
8

Express the following as percentages:

a

8

b

4

c

2.5

d

1.89

e

10

f

5.09

g

3.125

9

Which is greater: 0.26 or 35\%?

10

Write either <, > or = between the pair of numbers to make the following statements true:

a

\dfrac{1}{3} ⬚ 27\%

b

16\% ⬚ \dfrac{4}{25}

c

\dfrac{1}{8} ⬚ 13\%

Mixed numbers and percentages
11

Express the following mixed numbers as percentages:

a

1\dfrac{4}{5}

b

3\dfrac{7}{10}

c

5\dfrac{1}{4}

d

2\dfrac{7}{20}

12

State whether the following values are the same as 62\dfrac{1}{2}\%:

a

0.63

b

\dfrac{63}{100}

c

0.625

d

\dfrac{5}{8}

13

Express the following percentages as fractions in simplest form. Write your answer as mixed number if necessary.

a

275\%

b

107\%

c

145\%

d

320\%

e

238\%

f

9\dfrac{3}{10}\%

g

27\dfrac{7}{9}\%

h

34.24\%

14

Convert the following to mixed number percentages:

a
\dfrac{2}{9}
b
\dfrac{2}{3}
c
0.\overline{5}
d
0.\overline{3}
15

Express 33\dfrac{1}{3}\% as a simplified fraction.

Compare fractions, decimals and percentages
16

Convert between percentages, fractions and decimals to complete the following tables:

a
b
c
d
17

For the following groups of numbers:

i

Rewrite the group as percentages

ii

Hence write the numbers in ascending order.

a
\dfrac{5}{10},\, 100\%,\, 0.3
b
\dfrac{1}{4},\, 60\%,\, 0.3
c
\dfrac{3}{8},\, 20\%,\, 0.8
d
\dfrac{2}{5},\, 38\%,\, 0.49
Applications
18

A bushfire moves through an area of land. If 25\% of the land is burned by the bushfire, what proportion of the land, as a decimal, is not burned?

19

Irene spends 27\% of her pocket money each week.

a

Express how much of her pocket money she spends as a decimal.

b

Express how much of her pocket money she saves as a decimal.

20

a