In mathematics, rational numbers are represented in the form of p/q, where p and q can be any integer and q ≠ 0 (cannot equal 0). This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).
Types of Rational Numbers in Maths
- Integers like -2, 0, 3, etc., are rational numbers.
- Fractions whose numerators and denominators are integers like 3/7, -6/5, etc., are rational numbers.
- Terminating decimals like 0.35, 0.7116, 0.9768, etc., are rational numbers.
- Non-terminating decimals with some repeating patterns (after the decimal point) such as 0.333…, 0.141414…, etc., are rational numbers. These are popularly known as non-terminating repeating decimals.
Examples of Rational Numbers
If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number. Some examples of rational numbers are as follows:
- 56 (which can be written as 56/1)
- 0 (which is another form of 0/1)
- 1/2
- √16 which is equal to 4
- -3/4
- 0.3 or 3/10
- -0.7 or -7/10
- 0.141414… or 14/99
Rational numbers can be easily identified with the help of the following characteristics:
- All integers, whole numbers, natural numbers, and fractions with integers are rational numbers.
- If the decimal form of the number is terminating or recurring as in the case of 5.6 or 2.141414, we know that they are rational numbers.
- In case, the decimals seem to be never-ending or non-recurring, then these are called irrational numbers. As in the case of √5 which is equal to 2.236067977499789696409173… which is an irrational (not rational) number.
- Another way to identify rational numbers is to see if the number can be expressed in the form p/q where p and q are integers and q is not equal to 0.
How to Identify Rational Numbers with Examples
Example 1: Is 0.923076923076923076923076923076… a rational number?
- Solution: The given number has a set of decimals 923076 which is recurring and repeated continuously. Thus, it is a rational number.
Example 2: Is √2 a rational number?
- Solution: If we write the decimal value of √2 we get √2 = 1.414213562….which is a non-terminating and non-recurring decimal. Therefore, this is not a rational number. It is an irrational number.
