Large Number
\(1500 = 1.5 \times 10^3\)
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Scientific Notation & Significant Figures
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
- Format: a × 10^n where 1 ≤ |a| < 10
- Positive exponent: Number is large (move decimal right)
- Negative exponent: Number is small (move decimal left)
- Significant figures: Digits that carry meaning in precision
Significant Figures Rules:
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Leading zeros are not significant
- Trailing zeros after decimal point are significant
\(a \times 10^n\) where \(1 \leq |a| < 10\)
Worked Examples
Small Number
\(0.0025 = 2.5 \times 10^{-3}\)
Significant Figures
\(3.14159 \rightarrow 3.14\) (3 sig figs)