How do I convert a decimal number into a fraction?

All decimal numbers can be converted into fractions as long as they are rational numbers. For instance, the number `pi` is an irrational number and so it can’t be written as a fraction. The following procedure is not difficult. It starts by putting the decimal part of the number (the digits on the right of the dot) on the numerator of a fraction and we put number 1 as being the denominator. Then, so as to obtain an equivalent fraction without decimal numbers, we multiply the numerator and the denominator by 10, 100, 1000... according to the number of digits of the decimal part, this is, if the decimal part has one digit, we will multiply by 10; if it has two digits, we will multiply by 100 and so forth. Finally, if the obtained fraction is not irreducible, it is simplified. Let’s see some examples so as to be easier to understand the concept:

Convert number 0.2 into a fraction

`(0.2)/1 = (0.2 xx 10)/(1 xx 10) = 2/10 = 1/5`

Convert number 0.75 into a fraction

`(0.75)/1 = (0.75 xx 100)/(1 xx 100) = 75/100 = 3/4`

Convert number 0.625 into a fraction:

`(0.625)/1 = (0.625 xx 1000)/(1 xx 1000) = 625/1000 = 5/8`

Convert number 2,35 into a fraction

`2 + (0.35)/1 = 2 + (0.35 xx 100)/(1 xx 100) = 2 + 35/100 = 2 + 7/20 = 40/20 + 7/20 = 47/20`

And what will I have to do if I want to convert a number from fraction to a decimal one?

That conversion is much easier! Having in mind that the stroke of a fraction stands for a division, it will be enough to divide the numerator by the denominator if you want to convert from a fraction to a decimal. For instance: `5/2 = 5 : 2 = 2.5`.

Check out our List of Questions to get to know a little more about the most diverse topics related to mathematics. If you have any pertinent (math) question whose answer can not easily be found, send us an email on the Contact page with the question. We will be happy to respond. In the event that you detect any errors in our answers, do not hesitate to contact us!