Maths - Rational numbers tutorial 1

Tell your friends

A rational number is any number that can be written in the form:

\frac{p}{q} \quad \text{where } p, q \in \mathbb{Z} \text{ and } q \neq 0

p = numerator
q = denominator

(a) $\frac{3}{4}$ (b) $-\frac{7}{5}$ (c) $2 = \frac{2}{1}$ (d) $0 = \frac{0}{1}$

(i) $\sqrt{2}$ (ii) $\pi$ (iii) $0.333\ldots$ (recurring without pattern)

Types of Rational Numbers

All integers are rational numbers:
$-3 = \frac{-3}{1}, \quad 5 = \frac{5}{1}$

Proper fraction: $\frac{3}{5}$ Improper fraction: $\frac{7}{4}$ Mixed number: $1\frac{3}{4}$

Decimals that end:
$0.25 = \frac{1}{4}, \quad 0.6 = \frac{3}{5}$

Decimals with a repeating pattern:
$0.\overline{3} = \frac{1}{3}, \quad 0.\overline{12} = \frac{4}{33}$

Divide numerator by denominator.

\frac{3}{4} = 0.75

Write over a power of 10 and simplify.

0.2 = \frac{2}{10} = \frac{1}{5}

Let the number equal (x).

x = 0.\overline{6}

10x = 6.\overline{6}

10x - x = 6

9x = 6 \Rightarrow x = \frac{2}{3}