Exercise 38
Decimals, Fractions and Percentages
At the end of this exercise you will:
• Be able to convert percentages to fractions.
• Be able to convert percentages to decimals.
• Be able to convert fractions to percentages.
• Be able to convert fractions to decimals.
• Be able to convert decimals to fractions.
• Be able to convert decimals to percentages.
Answers on page 5, of this exercise.
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Decimals, Fractions and Percentages
Decimals, fractions and percentages can be described as being part of a whole one.
They are just different ways of writing parts of a whole one and as such are
interchangeable with each other.
To show you how the three different parts are similar have a look at the table below
which includes a picture showing the amount:
Decimal
Fraction
Percentage
0.25
¼
25%
0.5
½
50%
0.75
¾
75%
0.3333333
⅓
33⅓%
0.6666667
⅔
66⅔
Picture
There two numbers above that look out of place they are the 0.3333333 and the
0.6666666, that is because some decimals do not work out fully.
This is because the 3 and the 6 are what we call ‘recurring decimals’, the numbers
will go on forever.
So when this happens we will have worked the number to a specific number of
decimal places; such as 3 decimal places.
Or, with the 0.6666666 we can round up the number like so 0.667, there is another
way to cut short the number and that is to put an apostrophe (‘) after the number, this
means that the number is a recurring decimal i.e. 0.333333 becomes 0.33’.
(Its makes life a lot easier than trying to work out where to stop with the number.)
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How to convert Decimals to Fractions to Percentages
Decimals to fractions this is the tricky one of the three. The decimal has to be
exact and not rounded up or down, for you to get the correct fraction.
To convert percentages to fraction, simply divide the percentage by 100 as shown
below.
25% ÷ 100 = 25 = 1
100 4
To convert fractions to percentages, simply multiply the fraction by 100 as shown
below.
3 x 100 = 3 x 25 = 75%
4
To convert a decimal to a fraction, simply divide the decimal by the required value as
shown below. (i.e. put a 1 below the decimal point and then a nought for ever number
after the decimal point.)
0.25 = 1
100 4
0.0125 = 1
10000 8
To convert a fraction (¾) into a decimal divide the bottom number into the top
number, as shown below.
4 3 . 0 20
0 . 7 5 so ¾ = 0.75
To convert a percentage (75%) into a decimal, divide it by 100, as shown below.
100 75%
100 75.00
0.75
To convert a decimal (0.25) into a percentage times it by 100, as shown below.
0.25
x 100
02500 = 25.00% = 25%
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Now have a go at filling in missing values of the table below including
the written word, the first one is done for you.
Decimal
Fraction
Percentage
0.25
¼
25%
Nought point two
five
Quarter
Twenty-five percent
Picture
½
75%
33⅓%
0.67
15%
1
8
0.1
80%
5
100
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Answers
Decimal
0.25
Fraction
¼
Percentage
25%
Nought point two
five
Quarter
Twenty-five percent
0.5
½
50%
Nought point five
Half
Fifty percent
0.75
¾
75%
Nought point
Three quarters
Seventy-five percent
0.33’
⅓
33⅓%
Nought point
three three
0.67
One third
Thirty-three and a
third
Nought point six
seven
⅔
66⅔%
Two thirds
sixty-six and two
thirds
0.15
3
20
15%
Nought point one
five
0.125
Nought point one
two five
0.1
Nought point one
Picture
Fifteen percent
three twentieths
1
8
one eight
1
10
12½%
Twelve and half
percent
10%
Ten percent
One tenth
0.8
Nought point
eight
0.05
Nought point
nought five
4
5
80%
Eighty percent
Four fifths
5
100
5%
Five percent
Five hundredths
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