Question

Decimal expansion of which of the following is non-terminating recurring?
1) 2/5
2) 3/16
3) 3/11
4) 137/25​

Answer 1

Answer:

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

1) 2/5

2) 3/16

3) 3/11

4) 137/25

ans= 1

Answer 2

Answer:

3/11 is a non terminating and recurring decimal

Explanation:

Given that:-

1)2/5 =(2/5)×(2/2)=(2×2)/(5×2)=4/10=0.4

It is a terminating decimal.

2)3/16

=3/(2×2×2×2)

=3/2⁴

=>(3/2⁴)×(5⁴/5⁴)

=>(3×5⁴)/(2⁴×5⁴)

=>(3×625)/10⁴

=>1875/1000

=>0.1875

It is a terminating decimal.

3)3/11

the denominator is not in the form of 2^m5^n

3/11 is not terminating decimal and it is a non terminating recurring decimal.

4)137/25

=>137/5²

=>(137/5²)×(2²/2²)

=>(137×4)/(5²×2²)

=>548/10²

=>548/100

=>5.48

It is a terminating decimal.