How do you convert decimals and whole numbers into fractions?

1 Answer
Apr 1, 2016

Follow the following process.


There are two types of decimals, which can be converted into decimals - (i) terminating decimals and (ii) non-terminating but repeating decimals. Non-terminating and non-repeating decimals cannot be converted to fractions, they are in fact irrational numbers.

Terminating decimals are easy to convert into fractions. Just note the place of last digit of the number after decimal point. Say for example let us consider the number #10.23456789#, in which last digit #9# after decimal is at eighth position after decimal point. Hence #10.23456789=1023456789/100000000#. This may be simplified if possible by dividing numerator and denominator by a common number. As only prime factors of denominator are invariably #2# and #5#, if numerator is not divisible by this number (as in the given instance), then the fraction cannot be simplified further.

The process of converting non-terminating but repeating decimals is comparatively difficult and depends on which portion of the decimal part is repeating. The details can be found here.

Whole numbers are easiest to be converted into fractions. If the number is #x# just write it as #x/1# and then multiply numerator and denominator by any common desired number. For example, #16# can be written as #16/1=(16xx15)/(1xx15)=240/15#.