Converting Fractions, Decimals and Percentages

For your maths exam, you will be expected to be able to convert between fractions, decimals and percentages.  Often, you will also be asked to put these numbers in order from smallest to largest.  Read through the example below and try the test questions.

Example Question

a) Write 45% as a decimal and as a fraction in its simplest form.
b) Write 0.7 as a percentage and as a fraction in its simplest form.
c) Write 3/5 as a percentage and as a decimal.

d) Put these numbers in order of size, smallest first:
24%, 0.02, 13/50, 0.275, 1/5

Solution
a)
To convert from a percentage to a decimal divide by 100.
So 45% = 45 ÷ 100 = 0.45.

To convert to a fraction remember “per cent” means “out of 100” so:
45% = 45/100 = 9/20 in its lowest terms.

b)
To convert from a decimal to a percentage multiply by 100.
So 0.7 x 100 = 70%

Now as a fraction becomes:
70/100 = 7/10 in its lowest terms.

c)
In this case we start off with a fraction.  The trick is to try and make the denominator of the fraction equal to 10, 100 or 1000.

3/5 = 6/10 (multiply the numerator and denominator two.)

Now 6/10 = 6 ÷ 10 = 0.6.

And as a percentage:
0.6 x 100 = 60%

d)
Before we can write these numbers in order of size we must first convert them to the same type of number, i.e. fraction, decimal or percentage.
Note: Always convert to either decimals or percentages as these are the easiest to work out.
24%, 0.02, 13/50, 0.275, 1/5

For this example we will convert all the numbers to percentages.
  • 24% is already done for us!
  • 0.02 x 100 = 2%
  • 13/50 = 26/100 = 26%
  • 0.275 x 100 = 27.5%
  • 1/5 = 2/10 = 20%
So in order or size we have: 2%, 20%, 24%, 26%, 27.5%.
Test Yourself!

a) Write 64% as a decimal.
 
b) Write 0.12 as a fraction in its simplest form.
 
c) Write 8/25 as a percentage.
 
d) Put these numbers in order of size, smallest first.
    Give your answers as percentages.
42%, 0.4, 22/50, 0.405
% % % % 

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