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Q.

Examine whether the following number is rational or irrational:Question Image


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a

Rational

b

Irrational

c

Both a and b

d

None of these 

answer is A.

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Detailed Solution

Concept- To determine whether 7.478478... is a rational number or an irrational number, we shall resort to the definitions of rational and irrational numbers. If the number is rational, it can be expressed in ratio or fraction form; but, if the number is irrational, we are unable to do so.
It is given in theQuestion that we have to check whether the number Question Image is a rational number or irrational number.
We will now review the definitions of rational and irrational numbers in their most basic forms. Therefore, the ratio between two integers that are expressed in fraction form is what constitutes a rational number. Question Image, the condition for q is that Question ImageAdditionally, a number that is not rational is referred to as an irrational number. Alternatively, we may say that a number that exists in decimal form but cannot be expressed in ratio or any other fraction form is an irrational number.
Several instances of rational numbers include Question Image etc., and some examples of irrational behavior
numbers are Question Image, etc.
Difference between rational numbers and irrational numbers:
Question ImageThe answer is 7.478478, which is a non-repeating and non-terminating decimal.
Additionally, there is no fractional representation allowed for non-recurring and non-terminating decimals.
Hence, the correct answer is option 1.
 Syllabus: CBSE
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Examine whether the following number is rational or irrational: