Definition of Rational Number

## "A rational number is a number which can be expressed in the form of p/q where p and q are integers and ‘q’ ≠ 0. p/q is in the lowest form, i.e. p and q have no common factors."

- Set of all Rational Number is denoted by 'Q'.
- Rational numbers (Q) are included in real numbers, and in turn include the integers (Z), which include the natural numbers (N).” Thus, integers as well as fractions can be expressed in this form. So, all Natural Numbers, integers and fractions are rational numbers.

**Note:** N ⊂ W ⊂ Z ⊂ Q

### Some of the following are the examples of rational numbers:

(i) 5/3 is a rational number of form p/q where p = 5 and q = 3.

(ii) Similarly, 1/9 is a rational number of form p/q where p = 1 and q = 9.

(iii) 2 (= 2/1) is a rational number of form p/q where p = 2 and q = 1. Also, 2 is a real number, a natural number, and an integer.

(iv) 0/5 (= 0) is a rational number of form p/q where p = 0 and q = 5.

Understand that every number has a decimal expansion; for rational numbers, show that the decimal expansion terminates or repeats, and convert a decimal expansion that repeats into a rational number.

Yes, You are right, we will expand this topic on the basis of decimal expansion.