Converting between Decimals Fractions and Decimals
Decimals, fractions and percentages are all different ways of saying a similar thing and you can convert between them.
Let’s look at some examples:
25% is the same as the fraction which simplifies to
(one quarter) is the same as the decimal 0.25.
So we just saw that 25% is the same as which is the same as 0.25.
Let’s look at some more:
10% = = 0.1
50% = = 0.5
80% = = 0.8
100% = = 1
Converting to Decimals
Converting Percentages to Decimals
To turn a percentage in to a decimal, simply take the percentage and divide it by 100:
66% = 0.6
The best way to divide by 100 is simply to move the decimal point 2 places left.
Converting Fractions to Decimals
To convert fractions to decimals you have to divide the top number in the fraction by the bottom number:
as a decimal is:
25 ÷ 100 = 0.25
Converting to Fractions
Converting Percentages to Fractions
Remember that percentages are out of 100.
Converting percentages to fractions is easy. The percentage is already out of 100. So we just need to write the percentage over 100:
If we want to simplify this we can by dividing top and bottom by 2:
Converting Decimals to Fractions
Converting a decimal to a fraction is a bit more tricky. You would only be asked to do this if the decimal had one or two decimal places.
Here is a method to follow:
- Multiply the decimal by 100 to turn it in to a percentage.
- Write the percentage as a fraction over 100 and simplify if needed.
Let’s look at writing 0.5 as a fraction:
You times the decimal by 100 changing it in to a percentage:
0.5 x 100 = 50%
Place the percentage over 100:
Next we simplify the fraction if needed, in this case we can divide top and bottom by 50 and simplify it to:
Converting to Percentages
Converting Decimals to Percentages
Converting decimals to percentages is easy, you simply multiply the decimal by 100.
0.3 = 30%
0.85 = 85%
Converting Fractions to Percentages
Converting fractions to percentages involves two steps:
- First change the percentage in to a decimal by dividing the top number by the bottom number.
- Then times the decimal by 100.
Let’s look at turning in to a percentage:
First we divide 4 by 10:
4 ÷ 10 = 0.4
Then we times by 100:
0.4 x 100 = 40%
Question: of the audience in a theatre are wearing spacesuits. What percentage of the audience is this?
To convert a fraction to a percentage we first change it to a decimal by dividing the top number by the bottom one:
1 ÷ 5 = 0.2
To do this in your head easily just multiply both numbers by 10 so that the sum is 10 ÷ 5 = 2 and then divide your answer by 10: 2 ÷ 10 = 0.2
Then we multiply 0.2 by 100:
0.2 x 100 = 20%