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2.01 Conversion between fractions, decimals and percentages

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
0.07\%
g
0.02\%
h
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{3}{8}

d

\dfrac{48}{73}

e

\dfrac{97}{250}

f

\dfrac{93}{150}

g

\dfrac{21}{35}

h

\dfrac{39}{60}

i

\dfrac{8}{15}

j

\dfrac{27}{32}

k

\dfrac{69}{80}

l

\dfrac{23}{64}

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
0.65\%
j
9.8\%
k
6.42\%
l
736.5\%
m
18.41\%
n

303\%

o

270\%

p
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
0.411
k
0.274
l
0.876
8

Express the following as percentages:

a

8

b

4

c

1.1

d

2.5

e

1.89

f

10

g

5.09

h

3.125

i

4.64

j

3.075

k

11.4

l

2.099

9

Which is greater: 0.26 or 35\%?

Mixed numbers and percentages
10

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}

11

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}

12

Express the following percentages as fractions in simplest form. Write your answer as mixed numbers 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\%

13

Convert the following to mixed number percentages:

a
\dfrac{2}{9}
b
\dfrac{2}{3}
c
0.\overline{5}
d
0.\overline{3}
14

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

Compare fractions, decimals and percentages
15

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

a
FractionDecimalPercentage
\dfrac{11}{100}
1.83
\dfrac{5}{8}
b
FractionDecimalPercentage
\dfrac{1}{2}
0.75
30\%
c
FractionDecimalPercentage
\dfrac{3}{5}
0.32
72\%
d
FractionDecimalPercentage
1\dfrac{2}{5}
3.56
112\dfrac{1}{2}\%
16

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
17

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?

18

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

a

Express how much of her pocket money she spends as a:

i

Fraction

ii

Decimal

b

Express how much of her pocket money she saves as a:

i

Fraction

ii

Decimal

19

Patricia and Nadia are among the candidates for a school leadership position. Patricia receives 0.3 votes for every vote cast and Nadia receives 0.6 votes for every vote cast.

a

What was the combined percentage of votes for Patricia and Nadia?

b

What percentage of votes did not go to Patricia?

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