Question

Which of the following is an irrational number?(a)3.14 (b)3.1414... (C)3.14444....... (D)3.141141114

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following is an irrational number

(a)3.14

(b)3.1414...

(C)3.14444....

(D)3.141141114...

CONCEPT TO BE IMPLEMENTED

Rational Number

A Rational number is defined as a number of the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

A number which is not rational number is called irrational number

EVALUATION

First number : 3.14

Above number can be rewritten in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So the number is rational number

Second number : 3.1414...

$\sf{3.1414... = 3. \overline{14}}$

Above number can be rewritten in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So the number is rational number

Third number : 3.14444....

$\sf{3.14444.. = 3.1 \bar{4}}$

Above number can be rewritten in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So the number is rational number

Fourth number : 3.141141114

Above number cannot be rewritten in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So the number is irrational number

FINAL ANSWER

Hence the correct option is

(D)3.141141114...

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Answer 2

Step-by-step explanation:

Above number can be rewritten in the form \displaystyle \sf{ \frac{p}{q} \: }

q

p

Where p & q are integers with q ≠ 0

So the number is rational number

Second number : 3.1414...

\sf{3.1414... = 3. \overline{14}}3.1414...=3.

14

Above number can be rewritten in the form \displaystyle \sf{ \frac{p}{q} \: }

q

p

(D)3.141141114