Choose the correct alternative answer for the question given below.

Decimal expansion of which of the following is non-terminating recurring ?

#### Options

`2/5`

`3/16`

`3/11`

`137/25`

#### Solution

1) Since ,`5 = 2^0 xx 5^1` , which is in the form of `2^m xx 5^n`, where m and n are non - negative integers.

So, the decimal expansion of `2/5` is terminating.

2) Since , `16 = 2^4 xx 5^0`, which in the form of `2^m xx 5^n` , where m and n are non - negative integers.

So, the decimal expansion of `3/16` is terminating.

3) Since , `11 = 2^0 xx 5^0 xx 11^1`, which is not in the form of `2^m xx 5^n`, where m and n are non - negative integers.

So, the decimal expansion of `3/11` is non - terminatingrecurring.

4) Since , `25 = 2^0 xx 5^2` , which is in the form of `2^m xx 5^n`, where m and n are non - negative integers.

So, the decimal expansion of `137/25` is terminating.