Question

Define rational number with example.

Answer 1

Hint: Rational numbers are those numbers that can be expressed as a quotient (the result in a regular division equation) or in the format of a simple fraction. Even if you express the resulting number not as a fraction and it repeats infinitely, it can still be a rational number. Zero is a rational number.

Complete step by step answer:

Rational Number Definition
A rational number is any number that satisfies the following three criteria:
(i) It can be expressed in the form of a simple fraction with a numerator (p) divided by a (/) a denominator (q).
(ii) Both the numerator and the denominator must be regular integers themselves. An integer is what we would normally call a "whole number" like \[{\text{3}}\] or \[{\text{15}}\]. It can be positive or negative.
(iii) The denominator (q) cannot be zero.
(iv) Any number divided by zero (i.e., where the denominator is zero) approaches infinity (or negative infinity), but is undefined.

Zero Is a Rational Number.

With this explanation in mind, you can see how zero (\[0\]) is a rational number. That's because while there is a restriction on the denominator (the "bottom" number in a fraction), there is no similar restriction on the numerator (the "top" number in a fraction).

Note:
If the numerator is zero (\[0\]), and the denominator is any non-zero integer, the resulting quotient is itself zero.
(i) \[\dfrac{0}{5} = 0\]
(ii) \[\dfrac{0}{{200}} = 0\]