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.

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