Question

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

Options

• `2/5`

• `3/16`

• `3/11`

• `137/25`

Answer 1

`bb(3/11)`

Explanation:

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-terminating recurring. 

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.