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
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