Question

2.12112111211112.................... is
1 ) rational no.
2) integer
3)none of these
4) irrational​

Answer 1

Answer:

4) → irrational number

Step-by-step explanation:

2.12112111211112................ is a irrational number because the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers

Answer 2

The correct answer is option 4) irrational.

Given:

The number 2.12112111211112......

To Find:

The nature of the given number.

Solution:

To find the correct answer to this question, we will first have to understand what rational and irrational numbers are.

Rational numbers:

Rational numbers are those that can be expressed in the form of a ratio or a fraction.

It has the form p/q, where q is non-zero.

Rational numbers have terminating or recurring decimals.

Eg. 5 (as 5 = 5/1), 0.5, 83/2, etc.

Irrational numbers:

Irrational numbers are the ones that cannot be represented as a decimal or a fraction.

In terms of a decimal, it has non-repeating and non-terminating values.

Eg. π, √2, √3, 7/0, etc.

Let us analyze the number 2.12112111211112....

We observe that the digits after the decimal point are non-repeating and non-terminating. Hence, from the above properties, the given number is irrational.

The correct answer is option 4) irrational.

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