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Concept of Rational Numbers

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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.

notes

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 `-3/4`is neither an integer nor a fractional number. We need to extend our number system to include such numbers. So, we need rational numbers.
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