Examiners can ask for basic numerical computation. Get fluent with the half-dozen techniques below.
Percentages
- Of a total: 23 out of 60 participants recalled all words → 23/60 × 100 = 38.3%.
- Increase / decrease: scores rose from 12 to 15 → change = 3 → 3/12 × 100 = 25% increase.
Fractions and decimals
Convert between equivalent forms:
- 7/20 = 0.35 = 35%.
- 0.625 = 5/8 = 62.5%. When comparing, convert to the same form (usually decimals).
Ratios
A ratio expresses two quantities in simplest form. A group has 18 girls and 12 boys → divide by 6 → 3 : 2. Useful for sample composition and stratified sampling.
Significant figures (s.f.)
The meaningful digits of a number, starting with the first non-zero digit.
- 0.0042 → 2 s.f.
- 1023 to 3 s.f. → 1020.
- 0.45678 to 3 s.f. → 0.457 (round 5–9 up).
Use 2–3 s.f. when reporting summary statistics.
Decimal places (d.p.)
Number of digits after the decimal point.
- 0.45678 to 2 d.p. → 0.46.
- 12.503 to 1 d.p. → 12.5.
Scientific notation
Writing numbers as a × 10ⁿ where 1 ≤ a < 10.
- 4,500,000 → 4.5 × 10⁶.
- 0.000067 → 6.7 × 10⁻⁵. Helpful for very large or very small numbers (e.g. neuron counts, reaction-time fractions).
Order of magnitude
The power of 10 nearest to a number. 850 has order of magnitude 10³ (since 10³ = 1000 is closer than 10² = 100). Used to compare values of very different size.
✦Worked example
A study reports a mean reaction time of 0.4567 seconds.
- To 2 d.p.: 0.46 seconds.
- To 2 s.f.: 0.46 seconds.
- In scientific notation: 4.567 × 10⁻¹ seconds.
- As a fraction of one second: ~0.46 or ~46/100.
- Order of magnitude: 10⁻¹ (close to 1 second).
⚠Common mistakes— Common errors
- Multiplying by 100 to get a percentage but forgetting to divide by the total first.
- Confusing s.f. with d.p. (especially for numbers like 0.0042).
- Writing scientific notation with the multiplier outside 1–10 (e.g. "12 × 10²" should be 1.2 × 10³).
AI-generated · claude-opus-4-7 · v3-deep-psychology