Rational and Irrational Numbers

# Rational and Irrational Numbers

GCSE(F), GCSE(H),

A rational number can be written as a fraction. It can be written either as a proper fraction (for example, frac(1)(3)) where the denominator is larger than the numerator; or as an improper fraction (for example, frac(12)(5)).

(Higher Students: recurring decimals can be written as a fraction, and are therefore rational: see Recurring Decimals).

An irrational number cannot be written as a fraction. Examples of irrational numbers include π and √2.

## Examples

1. Is (π ÷ 4) a rational number?

Answer: No, because π is not a rational number.

2. Is -sqrt(0.25) a rational number?

Answer: Yes, because it can be written as -frac(1)(2)

-sqrt(0.25)

= -(0.5)

= -frac(1)(2)

Because it can be written as a fraction, it is a rational number.