Arithmetic and Significant Figures
High-Yield Summary
- Scientific notation: coefficient (1–10) × 10^exponent. Decimal shifts left → positive exponent; shifts right → negative exponent.
- Sig figs: all non-zero digits count; zeros between significant digits count; trailing zeros after a decimal point count; leading zeros never count.
- Rounding rule depends on the operation: multiplication/division → round to fewest sig figs among inputs; addition/subtraction → round to fewest decimal places among inputs.
- No calculator on the MCAT — estimate via balanced rounding: for multiplication, round one number up and the other down; for division, round numerator and denominator in the same direction.
Significant Figure Rules
| Rule | Example (sig figs) |
|---|---|
| All non-zero digits are significant | 247 → 3 sig figs |
| Zeros between significant digits are significant | 5006 → 4 sig figs |
| Trailing zeros after a decimal point are significant | 0.00560 → 3 sig figs |
| Leading zeros are never significant | 0.0056 → 2 sig figs |
Rounding: Multiplication/Division vs. Addition/Subtraction
| Multiplication or Division | Addition or Subtraction |
|---|---|
| Round to fewest sig figs among inputs | Round to fewest decimal places among inputs |
| 10.7 (3 sf) × 8.1 (2 sf) → round to 2 sig figs | 12.56 + 0.7 → round to 1 decimal place → 12.6 |
Common MCAT Trap
- Don't apply the sig-fig rule to addition/subtraction, or the decimal-place rule to multiplication/division — mixing these up is the single most common error on this topic.
- Leading zeros are never significant regardless of how many there are — 0.00056 still has only 2 sig figs (5 and 6).
Quick Recall
How many sig figs in 0.00560?
12.5 (3 sig figs) ÷ 2.0 (2 sig figs) — to how many sig figs should the result be rounded?