Tutor’s Toolkit: Application of Number

Carrying Out Calculations

C3	Convert between fractions, decimals and percentages

Useful Web Links:

Descartes 2D: Fractions, decimals and percentages
http://descartes.cnice.mecd.es/ingles/3rd_year_secondary_educ/Fract_dec_ptges/
This is a very comprehensive Spanish site, written in English, dealing with fractions, decimals and percentages.

BBC Skillswise: Numbers: Comparing decimals and percentages
http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/comparing/decimalspercentages/

BBC Skillswise: Numbers: Comparing fractions and decimals
http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/comparing/fractionsdecimals/

BBC Skillswise: Numbers: Comparing fractions and percentages
http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/comparing/fractionspercentages/

BBC Skillswise: Numbers: Comparing all three
http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/comparing/comparingall3/

C3.1	Convert between fractions, decimals and percentages

Scope: 

Students need to be able to:
•	Convert between fractions and percentages
•	Choose the largest (or smallest) quantity from a list of fractions, decimals and percentages.

What students need to know:

How to convert between fractions and percentages

•	The important thing to realise about fractions, decimals and percentages is that they are all different ways of writing the same thing. They are all fractions, really.

A percentage is a fraction which always has 100 underneath. (The number ‘underneath’ is called the denominator).
So, 23% is exactly the same as .

•	A decimal is a fraction with a denominator of 10, 100, 1000 etc. depending on how many decimal digits there are.

So, 0.7 is exactly the same as .

0.82 is exactly the same as .

0.713 is exactly the same as .

•	This means that converting between decimals and percentages is quite straightforward,

0.82 is exactly the same as , which is 82%

So, 0.82 = 82%. It’s just like pounds and pence!
0.7 = 70%
0.713 = 71.3%

•	To convert between fractions and percentages we need to be able to simplify – that means to make the denominator as small as possible). Or, we need to change the denominator to be 100.

 (Roughly 33%)

•	We can use these percentages as building blocks:

 etc.

•	The other way round, we need to simplify:

•	Sometimes we cannot divide, for example, 

Choose the largest (or smallest) quantity from a list of fractions, decimals and percentages.

•	The best fraction type to use for comparing is the percentage. So, of you have a list; change them all into percentages. Then you can easily put them in order of size.

Example Question
Write this list in order of size: 0.4, 39%, , 0.432, .

Solution

First we change everything to percentages:

0.4 = 40%

0.432 = 43.2%
=60%

So the list is: 40%, 39%, 25%, 43.2%, 60%

If we put this in order, we get: 25%, 39%, 40%, 43.2%, 60%

So the answer is:

, 39%, 0.4, 0.432,