Question

How do we write those fractions into decimal fraction, which continue endlessly?

Answer 1

Please see below.

Explanation:

The best way is use long division for all given fractions and identify in each fraction, when the numbers start repeating (after the decimal point). But this will be too long a process here and hence only results are referred here.

What we do is check the digits that are repeating and then just write them once and mark a bar over them.

The bar above a number or a set of numbers indicates that these digits repeat endlessly.

`3/18=(1xx3)/(6xx3)=1/6=0.1ul(6) ul(6) ul(6) .....=0.1bar6`

`16/99=0.ul(16)color(white)(1)ul(16)color(white)(1)ul(16)...........=0.bar(16)`

`13/12=1.08ul(3) ul(3) ul(3) .....=1.08bar3`

`5/27=0.ul(185)color(white)(1)ul(185)color(white)(1)ul(185).....=0.bar(185)`