Standard form
The standard form convention
Standard form (also called scientific notation) expresses any number as A × 10ⁿ where 1 ≤ A < 10 and n is an integer.
Edexcel uses standard form in science-context questions on Papers 2 & 3 (calculator) and non-calculator arithmetic on Paper 1.
Converting large numbers: shift the decimal left; n is positive. Example: 93,000,000 = 9.3 × 10⁷.
Converting small numbers: shift the decimal right; n is negative. Example: 0.000047 = 4.7 × 10⁻⁵.
Converting back: positive n → move decimal right; negative n → move left. Example: 2.06 × 10⁻³ = 0.00206.
Calculations in standard form (Paper 1 — non-calculator)
Multiplying: multiply the A values, add the exponents. Adjust if A ≥ 10. (3 × 10⁴) × (7 × 10³) = 21 × 10⁷ = 2.1 × 10⁸.
Dividing: divide the A values, subtract the exponents. (8.4 × 10⁶) ÷ (2 × 10⁻²) = 4.2 × 10⁸.
Adding/subtracting: convert to the same power of 10 first. 3.2 × 10⁵ + 4 × 10⁴ = 32 × 10⁴ + 4 × 10⁴ = 36 × 10⁴ = 3.6 × 10⁵.
Edexcel examiner style
Edexcel Paper 1 routinely asks you to:
- Order numbers given in standard form (convert to ordinary numbers to compare).
- Estimate a calculation involving standard form by rounding to 1 s.f. first.
- Give answers to a specified degree of accuracy.
Papers 2 & 3 use standard form in real-world contexts: planetary distances, atomic radii, population sizes, reaction rates.
⚠Common mistakes
- A not in range: writing 12 × 10³ instead of 1.2 × 10⁴.
- Sign error on n: 0.0053 → moving right 3 places → 5.3 × 10⁻³ (negative), not +3.
- Adding before converting to same index: 3 × 10⁵ + 4 × 10⁴ ≠ 7 × 10⁵.
- Calculator mode: on a Casio, standard form is entered as 3 [×10ˣ] 5 (not 3 × 10 ^ 5 which might round).
AI-generated · claude-opus-4-7 · v3-edexcel-maths