Rational Numbers

A number that can be expressed in the form ${\displaystyle \frac{p}{q}}$, where p and q are integers, and q is not equal to zero "q ≠ 0", is called a rational number. The numbers ${\displaystyle -\frac{2}{7},\frac{3}{8},3}$ etc., are rational numbers.

1. The word rational arises from the term ratio.

2. A number that can be expressed in the form ${\displaystyle \frac{\text{p}}{\text{q}}}$, where p and q are integers and q ≠ 0, is called a rational number. In ${\displaystyle \frac{\text{p}}{\text{q}}}$, the integer p is the numerator, and the integer q (q ≠ 0) is the denominator. Thus, in ${\displaystyle \frac{-3}{7}}$, the numerator is - 3, and the denominator is 7.

3. All Fractional numbers are rational numbers. For example, ${\displaystyle \frac{3}{7},\frac{5}{8},\frac{0}{9},7\frac{1}{4},\frac{29}{4}}$ etc. are rational numbers.

4. All decimal numbers are rational numbers.

   ${\displaystyle 0.987=0.987\times \frac{1000}{1000}=\frac{0.987\times 1000}{1000}=\frac{987}{1000}}$.

5. All integers are rational numbers. For example, The integer - 5 is a rational number because you can write it as ${\displaystyle \frac{-5}{1}}$.
6. The integer 0 can also be written as 0 = ${\displaystyle \frac{0}{2}\text{or}\frac{0}{7}}$ etc. Hence, it is also a rational number.

• We can represent a distance of 750 m above sea level as ${\displaystyle \frac{3}{4}}$ km. But Can we denote the distance of ${\displaystyle \frac{3}{4}}$ km below sea level by ${\displaystyle -\frac{3}{4}}$?
• We can see ${\displaystyle -\frac{3}{4}}$is neither an integer nor a fractional number. We need to extend our number system to include such numbers. So, we need rational numbers.