Difference between rational and irrational numbers

Let us learn the difference between rational and irrational numbers,

A rational number is a number that can be written as a fraction.

The numerator and denominator of the fraction must be whole numbers.

A number that cannot be written as fraction is said to be an irrational number. Most irrational numbers contain surds (roots) and constants like Pi or e.

Example 1

Is 0.75 a rational or irrational number?

Well you can write 0.75 as ¾. So 0.75 is a rational number as it can be written as a fraction.

Example 2

Is 0.463 a rational or irrational number?

Again 0.463 can be written as a fraction as 463/1000. So 0.463 is a rational number.

Example 3

Is 0.3˙ a rational or irrational number?

Yes it is a rational number as 0.3 recurring is 1/3.

Example 4

Is 13 a rational or irrational number?

All whole numbers can be written as fraction, as you can make the denominator equal to 1 (13/1). So 13 is a rational number.

Example 5

Is √9 a rational or irrational a number?

√9 is 3, and 3 can be written as 3/1. So √9 is a rational number.

All the examples so far have been rational numbers (in fact most numbers are rational).

Hope the above explanation helped you.