Scientific Notation

A number in scientific notation: $a \times 10^n$ where $1 \leq a < 10$.

Examples:

• $45,000 = 4.5 \times 10^4$
• $0.003 = 3 \times 10^{-3}$
• $6,020,000 = 6.02 \times 10^6$

Operations with Scientific Notation

Multiply: $(3 \times 10^4)(2 \times 10^5) = 6 \times 10^9$

Divide: $\frac{8 \times 10^7}{4 \times 10^3} = 2 \times 10^4$

Square Roots and Cube Roots

$\sqrt{x} = x^{1/2} \qquad \sqrt[3]{x} = x^{1/3}$

$\sqrt{36} = 6 \qquad \sqrt[3]{27} = 3 \qquad \sqrt[3]{-8} = -2$

Simplifying Square Roots

$\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$

$\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}$

Tip: Find the largest perfect square factor when simplifying radicals.