Question

Which of the following is irrational ?(a)0.14(b)0.14161616(c)0.141614161416(d)0.4014001400014

Answer 1

Answer:

d)0.4014001400014

because it is in the form of recurring decimals

Answer 2

0.4014001400014 is an irrational number. (d).

Given,

4 options.

(a) 0.14

(b) 0.14161616

(c) 0.141614161416

(d) 0.4014001400014

To Find,

The irrational number from the given options.

Solutions,

For (a) 0.14

It is terminating so this is rational, not irrational.

For (b) 0.14161616

It is repeating so this is rational, not irrational.

For (c) 0.141614161416

It is repeating so this is rational, not irrational.

For (d) 0.4014001400014

It is non-repeating and non-terminating so this is irrational.

Hence, 0.4014001400014 is an irrational number. (d).

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