Question

Is 6.56556555... a rational or irrational number?

Choose the correct answer below.
irrational number
O rational number

Answer 1

The number 6.56556555... is an irrational number

What are irrational numbers?

Unlike rational numbers, which can be expressed as a ratio of two integers, irrational numbers cannot be represented as a finite or repeating decimal. Their decimal expansions go on forever without repeating,

Hence, 6.56556555... is an irrational number. An irrational number is a number that cannot be expressed as a finite or repeating decimal. The decimal representation of 6.56556555... goes on forever without repeating, making it an irrational number.

Answer 2

Irrational number

Explanation:

A number which can be written in the form of a fraction
`(p)/(q)`, is a rational number.

Examples :
`(1)/(2), (3)/(4), 1.41414141....`

In 1.41414141..... (41) is the repeating numbers after decimal. Therefore, it's a rational number.

Irrational numbers can't be written in the form of
`(p)/(q)`.

Examples : π, √3, 1.41456......

Given number in the question is 6.56556555....

In this number numbers after decimal are not repeating.

Therefore, given number is irrational.