Unit 4 Section 4 : Fraction, Decimal and Percentage Equivalents

In this section we revisit the equivalence of fractions, decimals and percentages;

for example, we could writeas 0.5 or as 50%.

Example 1

Write each of the following percentages as decimals and fractions in their simplest form:

(a) 75%
(b) 32%

Example 2

Write each of the following decimals as a percentage and as a fraction in its simplest form:

(a) 0.72
(b) 0.08

Example 3

Write each of the following fractions as a decimal and as a percentage:

(a)
(b)
(c)

Exercises

Give the fractions in the simplest form on this page.
Question 1
Write each of the following percentages as a decimal:
(a)60%
(b)70%
(c)20%
(d)45%
(e)31%
(f)82%
(g)14%
(h)4%
(i)63%
(j)2%
(k)1%
(l)19%
Question 2
Write each of the following percentages as a fraction in its simplest form:
(a)80%
(b)25%
(c)40%
(d)35%
(e)65%
(f)4%
(g)64%
(h)82%
(i)28%
(j)6%
(k)7%
(l)92%
Question 3
Write each of the following decimals as a percentage:
(a)0.74
(b)0.99
(c)0.5
(d)0.06
(e)0.26
(f)0.02
(g)0.3
(h)0.002
(i)0.042
Question 4
Write each of the following decimals as a fraction in its simplest form:
(a)0.5
(b)0.25
(c)0.4
(d)0.7
(e)0.62
(f)0.44
(g)0.37
(h)0.04
(i)0.05
(j)0.24
(k)0.1
(l)0.74
Question 5
Write each of the following fractions as a decimal:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
Question 6
Write each of the following fractions as a percentage:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
Question 7
Complete this table of equivalent fractions, decimals and percentages:
FractionDecimalPercentage
0.68
85%
0.76
3%
0.005
Question 8
In a survey, 400 people were asked how they would vote at the next election.
Express these results as percentages.
The results are listed below:
Labour 220
Conservative 160
Other 20
Question 9
In a school there are 50 Manchester City supporters out of a total of 2000 pupils.
(a) What percentage of the pupils support Manchester City?
(b) What percentage of the pupils do not support Manchester City?
Question 10
In a group of 40 pupils there are 7 who cannot swim.
What percentage of the pupils can swim?
Question 11
Simon is growing vegetables in three vegetable patches.
(a)
About 50% of this vegetable patch is for carrots.
Write down the missing percentages:
(i) about of the patch is for cabbages,
(ii) about of the patch is for lettuces.
(b)
Aboutof this vegetable patch is for beetroot.
Write down the missing fractions:
(i) about of the patch is for broad beans.
(ii) about of the patch is for peas.
(c)
Aboutof this vegetable patch is for potatoes.
Shade in the area for potatoes.
The rest of the patch is for turnips.
About what fraction of the patch is for turnips?
Question 12
of the diagram below is shaded.
(a)
Look at this diagram:
What fraction is shaded?
What percentage is shaded?
(b)
Shade of the diagram below.
What percentage of the diagram have you shaded?