Question

0.23456738910017... is an irrational number? TRUE/FALSE (WITH REASON)​

Answer 1

SOLUTION

TO CHECK

True / False below statement :

0.23456738910017... is an irrational number

EVALUATION

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

Where p & q are integers with $q \ne \: 0$

Also a number which is not rational number is called irrational number

Here the given number is

0.23456738910017...

Now the number can not be rewritten in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

So the number 0.23456738910017... is irrational

Hence the statement is TRUE

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Answer 2

Given :- 0.23456738910017... is an irrational number ? TRUE/FALSE (WITH REASON)

Answer :-

we know that,

• An irrational number is the real number which can be written in the form of fraction , p/q, where q ≠ 0 and which is Non terminating and non repeating .

given decimal number is , 0.23456738910017... which is Non terminating and non repeating decimal . { Digits after decimal are not repeating in same order . Ex :- 0.818181___ can be written as 0.(bar on 81) }

then,

→ 0.23456738910017... ≠ p/q .

therefore, we can conclude that, the given decimal number is an irrational number .

Hence, given statement is True .

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