Question

Classify the following as rational numbers and irrational numbers $0.6666......$

Answer 1

Definitions:

1. Rational number:

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.

2. Irrational number:

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio.

3. Non-terminating and recurring decimal numbers:

A non-terminating but recurring decimal is defined as a decimal that continues endlessly and repeats one or more numbers after the decimal point.

Example:

$\frac{10}{3}=3.333...$

Given data:

The given number is $0.6666.....$

Explanation:

Here, $0.6666....$ is a non-terminating and recurring decimal number.

As it continues endlessly and repeats one or more numbers after the decimal point.

Conclusion:

Since it is a non-terminating recurring decimal number then the given number is a rational number.

Final Answer:

$0.6666....$ is a rational number.