# Rational Numbers

#### definition

Rational Number: A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0, is called a rational number. The numbers -2/7, 3/8, 3 etc. are rational numbers.

# Rational Numbers:

• The word rational arises from the term ratio.

• A number that can be expressed in the form "p"/"q", where p and q are integers and q ≠ 0, is called a rational number.

• In "p"/"q", the integer p is the numerator, and the integer q (q ≠ 0) is the denominator.

• Thus, in (-3)/7, the numerator is - 3 and the denominator is 7.

• All Fractional numbers are rational numbers. For example, 3/7, 5/8, 0/9, 7 1/4, 29/4 etc. are rational numbers.

• All decimal numbers are rational numbers.

0.987 = 0.987 xx (1000)/(1000) = (0.987 xx 1000)/(1000) = (987)/(1000).

• All integers are rational numbers. For example, The integer - 5 is a rational number, because you can write it as (- 5)/1.
• The integer 0 can also be written as 0 = 0/2 or 0/7 etc. Hence, it is also a rational number.

## Need for Rational Numbers:

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