What Is a Rational Number?

A rational number is a very important concept in mathematics that students often come across in middle school and use throughout higher studies. To understand it in a simple way, let us break it down step by step.

Definition

A rational number is any number that can be written in the form of a fraction, where the numerator (the top part) and the denominator (the bottom part) are both integers and the denominator is not zero. In simple words, a rational number looks like this:

Rational Number = p/q, where q ≠ 0

• p is the numerator (can be positive, negative, or zero).
• q is the denominator (must be a non-zero integer).

For example, numbers like 2/3, -5/7, 10/1, and even whole numbers like 6 (which can be written as 6/1) are all rational numbers.

Examples to Understand Rational Numbers

• Fraction form: 7/9 is rational because both 7 and 9 are integers, and 9 is not zero.
• Integer form: -4 is also rational because it can be written as -4/1.
• Decimal form: Some decimals can also be rational numbers. For example, 0.5 is rational because it equals 1/2.

Key Features of Rational Numbers

• Rational numbers include positive numbers, negative numbers, and zero.
• They can be expressed in decimal form, but these decimals will either terminate (end after some digits, like 0.25) or repeat (like 0.333...).
• Rational numbers are a part of the larger set of real numbers, which also includes irrational numbers.

Difference Between Rational and Irrational Numbers

• Rational number: can always be written as a fraction p/q.
• Irrational number: cannot be written in fraction form. Examples include π (pi) and √2. Their decimal forms go on forever without repeating.

Why Are Rational Numbers Important?

Rational numbers are widely used in daily life and mathematics:

• When you divide money equally among people, you are dealing with rational numbers.
• Measurements in meters, liters, or weights can be fractions, which are rational numbers.
• Rational numbers are also used in algebra, coordinate geometry, and higher-level topics that form the base of competitive exams like JEE and NEET.