Scientific Notation

What is Scientific Notation?

A way to write very large or very small numbers: $a \times 10^n$

where $1 \leq |a| < 10$ and $n$ is an integer

Large Numbers

Example: $5,600,000 = 5.6 \times 10^6$

Move decimal left → positive exponent

Small Numbers

Example: $0.0000034 = 3.4 \times 10^{-6}$

Move decimal right → negative exponent

Converting to Standard Form

From scientific notation:

• Positive exponent → move decimal right
• Negative exponent → move decimal left

Examples:

• $4.2 \times 10^3 = 4,200$
• $7.8 \times 10^{-4} = 0.00078$

Operations

Multiplying

Multiply the numbers, add the exponents: $(3 \times 10^4) \times (2 \times 10^5) = 6 \times 10^9$

Dividing

Divide the numbers, subtract the exponents: $\frac{8 \times 10^7}{4 \times 10^3} = 2 \times 10^4$