Percentage to fraction

1.Convert percentage to fraction

The percentage is first converted into a decimal number by dividing it by 100.
Example:

`5.2% = 5.2\div100 = 0.052`

Then, convert the decimal number into a fraction with a denominator equal to a power of 10 i.e. 10, 100, 1000, 10000... Specifically,
For a number with one decimal (like 0.7), the denominator will be 10. Therefore, `0.7 = 7/10`
For a number with two decimals (like 0.64), the denominator will be 100. Therefore, `0.64 = 64/100`
For a number with three decimals (like 0.572), the denominator will be 1000. Therefore, `0.572 = 572/1000`, and so on...

Other examples:

`0.5 Rightarrow` remove decimal separator `Rightarrow 5` `Rightarrow` we divide by 10 because of 1 decimal `Rightarrow 5/10`

`0.12 Rightarrow` remove decimal separator `Rightarrow 12` `Rightarrow` we divide by 100 because of 2 decimals `Rightarrow 12/100`

`0.935 Rightarrow` remove decimal separator `Rightarrow 935` `Rightarrow` we divide by 1000 because of 3 decimals `Rightarrow 935/1000`

Coming back to our first example, we get,

`0.052 Rightarrow` remove decimal separator `Rightarrow 52` `Rightarrow` we divide by 1000 because of 3 decimals `Rightarrow 52/1000`

2.Simplify the resulting fraction

In this last step, we simplify the resulting fraction.

52/1000 is simplified with the GCD method,

GCD (52,1000) = 4

`52/1000 = (52\div4)/(1000\div4) = 13/250`

Therefore,

`5.2\% = 13/250`