Validity checks and exam traps
Big Idea: A standard form answer is not finished until the front number is at least 1 but smaller than 10.
This section shows the most common mistakes and how to fix them.
Common traps
- Coefficient is 10 or more.
- Coefficient is smaller than 1.
- Exponent sign is flipped.
- Calculator output is copied without correction.
| Incorrect form | Correct form | Fix |
|---|---|---|
| 31.5 × 10⁴ | 3.15 × 10⁵ | Divide coefficient by 10 and add 1 to exponent |
| 0.6 × 10⁸ | 6.0 × 10⁷ | Multiply coefficient by 10 and subtract 1 from exponent |
| 24.6 × 10⁴ | 2.46 × 10⁵ | Rewrite unfinished calculator form |
Exam wording recognition:
- "Write in standard form" means your final line must be valid a × 10ⁿ form.
- "Give your answer as an ordinary number" means convert back with correct zeros.
- "Explain why this is not valid" means mention the coefficient rule directly.
Marks protection:
- For 1 mark, a correct final line is usually enough.
- For 2-3 marks, show decimal movement or correction to secure method marks.
Reading GDC output as standard form
What your calculator actually shows: Your GDC cannot display × 10ⁿ — so it uses E notation instead.
5.24E8 means 5.24 × 10⁸.
Not valid in an IB exam: Writing 5.24E8 in your working scores zero for the answer — even if the number is correct.
Always rewrite before your final line.
| GDC screen shows | What it means | Write this |
|---|---|---|
| 5.24E8 | 5.24 × 10⁸ | 5.24 × 10⁸ |
| 1.78E-3 | 1.78 × 10⁻³ | 1.78 × 10⁻³ |
| 9.46E12 | 9.46 × 10¹² | 9.46 × 10¹² |
| 3.00E-7 | 3.00 × 10⁻⁷ | 3.00 × 10⁻⁷ |
The two-step habit: Step 1: Number before E → coefficient a.
Step 2: Number after E → exponent n.
Write: a × 10ⁿ and check 1 ≤ a < 10.
IB-style question
A population of bacteria starts at 500 and doubles every year.
After 20 years the population is 500 × 2²⁰.
Write this as a correct standard form answer rounded to 3 significant figures.
Step by step
- Type 500 × 2^20 into your GDC and press ENTER.
- Screen shows: 5.24288E8 — this is calculator notation, not a valid answer.
- Read the coefficient (number before E): 5.24288 → round to 3 s.f. → 5.24
- Read the exponent (number after E): 8
- Write in standard form:
Final answer
5.24 × 10⁸
What the examiner will not accept: ❌ 5.24E8 — calculator notation, zero marks for the answer
❌ 524 000 000 — ordinary form when standard form was asked
❌ 52.4 × 10⁷ — coefficient is not between 1 and 10
✅ 5.24 × 10⁸ — valid standard form, full marks
Partial credit: If your answer is correct but not in valid standard form (e.g. you write 524 000 000 or 52.4 × 10⁷), you keep the working mark but lose the answer mark. So the format costs you a real mark — not just a presentation issue.