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.