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 ($\mathbb{Q}$) $\frac{\text{integer}}{\text{integer}}$: $\frac{4}{7}, -3\frac{1}{8}, 0.3, 2.\dot{6}\dot{5}, 92, \sqrt{16}$

Irrational numbers: $\pi, \sqrt{2}, e$

Real numbers ($\mathbb{R}$): all numbers

🦉 Standard Form

A \times 10^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^m b^m

5.\,\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}

6.\,a^{-n} = \frac{1}{a^n}

7.\,a^0 = 1

8.\,a^\frac{1}{n} = \sqrt[n]{a}

9.\,a^\frac{m}{n} = (\sqrt[n]{a})^m