Scientific Notation
Format: a × 10ⁿ where 1 ≤ |a| < 10
Converting TO Scientific Notation
- Move the decimal point until you have a number between 1 and 10
- Count how many places you moved the decimal
- If you moved LEFT → positive exponent (large numbers)
- If you moved RIGHT → negative exponent (small numbers)
Examples:
45,000 → 4.5 × 10⁴ (moved 4 places left)
0.0032 → 3.2 × 10⁻³ (moved 3 places right)
Converting FROM Scientific Notation
- Look at the exponent
- Positive exponent → move decimal RIGHT
- Negative exponent → move decimal LEFT
- Fill in zeros as needed
Examples:
2.7 × 10⁵ → 270,000
8.1 × 10⁻⁴ → 0.00081
Significant Figures Rules
Rule 1: All non-zero digits are ALWAYS significant
123 → 3 sig figs | 7.89 → 3 sig figs
Rule 2: Zeros BETWEEN non-zero digits are ALWAYS significant
101 → 3 sig figs | 5.007 → 4 sig figs
Rule 3: Leading zeros are NEVER significant
0.0025 → 2 sig figs | 0.00100 → 3 sig figs
Rule 4: Trailing zeros AFTER a decimal point ARE significant
2.50 → 3 sig figs | 1.000 → 4 sig figs
Rule 5: Trailing zeros WITHOUT a decimal point are NOT significant (ambiguous)
1500 → 2 sig figs | 1500. → 4 sig figs (decimal makes it explicit)