Question

Which of the following is irrational no. (A) 0.15 (b) 0.01516 (c) 0.1516bar (d) 0.5015001500015......

Answer 1

Given:

$\mathbf{(a)= 0.15 \ \ (b)=0.01516 \ \ (c) =0.15161516... \ \ (d)=0.5015001500015...}$

To Find:

Which is irrational number ?

Solution:

Rational number:-

If decimal expansion of number terminate or non terminate but repeat some pattern. It will be rational number. Let us see option;

Option (a) = 0.15

Its decimal expansion is terminate, so it is rational number.

Option (b) = 0.01516

Its decimal expansion is terminate, so it is rational number.

Option (c) = 0.15161516...

Its decimal expansion is non-terminate but it is repeating. Repeating pattern are 1516. So it is rational number.

Irrational number:-

If decimal expansion of number is non terminate also non repeating of some pattern. It will be irrational number. Let us see option;

Option (d) = 0.15161516...

Its decimal expansion is neither non-terminate nor repeating. So it is irrational number.

So option d is irrational number.

Answer 2

Answer:

Option D

Step-by-step explanation:

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