Numbers & Their Operations

Types of numbers

Integers ( $\mathbb{Z}$ ): $..., -3, -2, -1, 0, 1, 2, 3, 4, ...$
Prime: integers that are divisible by 1 and itself only, smallest prime number is 2
Rational numbers ( $\mathbb{Q}$ ) $\dfrac{\text{integer}}{\text{integer}}$ : $\dfrac{4}{7}, -3\dfrac{1}{8}, 0.3, 2.\dot{6}\dot{5}, 92, \sqrt{16}$
Irrational numbers: $\pi, \sqrt{2}, e$
Real numbers ( $\mathbb{R}$ ): all numbers

Standard form

$A\times10^n$ , where $n$ is an integer, and $1\leq A<10$

SI prefix

$\begin{array}{|c|c|} \hline \text{Prefix} & 10^n\\ \hline \text{pico} & 10^{-12} \\\hline \text{nano} & 10^{-9} \\\hline \text{micro} & 10^{-6} \\\hline \text{milli} & 10^{-3} \\\hline \text{kilo} & 10^3 \\\hline \text{mega} & 10^6 \\\hline \text{giga} & 10^9 \\\hline \text{tera} & 10^{12}\\\hline \end{array}$

Indices

$1.\,a^m\times a^n=a^{m+n}$
$2.\,a^m\div a^n=a^{m-n}$
$3.\,(a^m)^n=a^{mn}$
$4.\,(ab)^m=a^mb^m$
$5.\,\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}$
$6.\,a^{-n}=\dfrac{1}{a^n}$
$7.\,a^0=1$
$8.\,a^\frac{1}{n}=\sqrt[n]{a}$
$9.\,a^\frac{m}{n}=(\sqrt[n]{a})^m$