Is the number 3.24636363…., a rational or irrational?

1.	Is the number 3.24636363…., a rational or irrational?
Answer» The given number is 3.24636363…. = \(3.24\bar{63}.\) (This number is non-terminating and repeating number which is a rational number. Because, a number is irrational only if the number has non-terminating and non-repeating decimal) second method :- Let x = 3.246363………. ⇒ 100x = 324.636363………. Now, 100x – x = 324.636363…. – 3.246363….. ⇒ 99x = 321.39 ⇒ x = \(\frac{321.39}{99}=\frac{32139}{9900}=\frac{3571}{1100}\) ⇒ x = \(\frac{3571}{1100}\) which is a rational number. Hence, 3.246363….. is a rational number.

Answer»

The given number is 3.24636363…. = \(3.24\bar{63}.\)

(This number is non-terminating and repeating number which is a rational number.

Because, a number is irrational only if the number has non-terminating and non-repeating decimal)

second method :- Let x = 3.246363……….

⇒ 100x = 324.636363……….

Now, 100x – x = 324.636363…. – 3.246363…..

⇒ 99x = 321.39

⇒ x = \(\frac{321.39}{99}=\frac{32139}{9900}=\frac{3571}{1100}\)

⇒ x = \(\frac{3571}{1100}\) which is a rational number.

Hence, 3.246363….. is a rational number.

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