Identifying Rational and Non – Rational Numbers - JSS3 Mathematics Lesson Note

Rational Numbers:

Rational numbers are numbers that can be expressed as a fraction of two integers (where the denominator is not zero). In other words, any number that can be written in the form 𝑝/𝑞, where 

𝑝 and 𝑞 are integers (whole numbers), and 

𝑞≠0, is a rational number. Rational numbers can also be written as terminating decimals or repeating decimals.

Examples of Rational Numbers:

0.75 (which is ¾  as a decimal)

0.333…. (which is ⅓ as a repeating decimal)

Non-Rational Numbers (Irrational Numbers):

Non-rational numbers, or irrational numbers, cannot be expressed as fractions of two integers. These numbers have decimal representations that neither terminate nor repeat. In simpler terms, they are numbers whose decimal expansions go on forever without settling into a repeating pattern.

Examples of Irrational Numbers:

𝜋 (approximately 3.14159265...)

𝑒 (approximately 2.71828183...)

0.101001000100001… (a decimal that neither repeats nor terminates)

Identifying Rational and Irrational Numbers:

To identify whether a number is rational or irrational, you can look at its decimal representation:

• If the decimal repeats or terminates, it is rational.
• If the decimal goes on forever without repeating, it is irrational.

For example:

0.5 is rational (terminating decimal).

3  is irrational (non-terminating, non-repeating decimal).