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S3 Maths: Significant Figures and Percentage Error (Paper 3 (challenge))
Tutor Prep Guide · Counting significant figures, rounding to significant figures, maximum absolute error, relative and percentage error, upper and lower limits, and rounding the result of a calculation
S3 Maths: Significant Figures and Percentage Error (Paper 3 (challenge))
Paper 3 (challenge): ten questions on significant figures and percentage error, with answers and one line notes.
Direct answers Level: S3 maths; format: judgement and calculation questions on significant figures and percentage error.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Significant Figures and Percentage Error |
| Level | S3 |
02 Questions (10 items)
- FoundationHow many significant figures does 0.4050 have?
- FoundationRound 9.995 to three significant figures.
- FoundationHow many significant figures do 20.0 and 1000 (no decimal point) have?
- IntermediateA rectangle measures 8.5 cm by 4.2 cm, each to the nearest 0.1 cm. Find the upper limit of its area to four decimal places.
- IntermediateA measurement has a percentage error of 0.5 per cent and a maximum absolute error of 0.2. Find the true value.
- IntermediateA length is recorded as 1.20 m with three significant figures. What is the maximum absolute error?
- ChallengeFor the same absolute error, why is the percentage error smaller when measuring a larger object?
- ChallengeA circle has a measured radius of 5.0 cm to the nearest 0.1 cm. Using π = 3.14, find the upper limit of its area to two decimal places.
- ChallengeA mass is written as 1000 g or as 1.000 kg. Which writing shows it was measured to the nearest gram?
- Error redoError clinic: a student rounds 0.0496 to one significant figure and writes 0.04. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Four | The figures 4, 0 and 5 plus the trailing zero after the decimal point give four significant figures. |
| 2 | 10.0 | Rounding up gives 10.0, and the decimal zero must be kept to show three significant figures. |
| 3 | 20.0 has three and 1000 has one | The trailing zero after the decimal point in 20.0 counts, while trailing zeros in a whole number such as 1000 usually do not. |
| 4 | 36.3375 cm² | Take both measurements at their upper limits: 8.55 times 4.25 gives 36.3375 square centimetres. |
| 5 | 40 | A percentage error of 0.5 per cent is 0.005, and 0.2 divided by 0.005 gives 40. |
| 6 | 0.005 m | Three significant figures means rounding to the nearest 0.01 m, so half of that is 0.005 m. |
| 7 | Because percentage error divides by the true value, so a larger true value gives a smaller ratio | Percentage error is the absolute error divided by the true value, so a larger denominator gives a smaller result. |
| 8 | 80.08 cm² | Take the radius upper limit 5.05, then 3.14 times 5.05 squared is 80.07785, which rounds to 80.08 square centimetres. |
| 9 | 1.000 kg, with four significant figures | 1000 g without a decimal point has only one significant figure, while the trailing zeros in 1.000 kg show precision to the nearest gram. |
| 10 | 0.05 | The first significant figure is 4 and the next digit 9 rounds it up to 5, giving 0.05. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Ask first whether a zero counts: zeros between non-zero digits, or trailing zeros after a decimal point, do count, while leading zeros that only mark place value do not. For error questions, write the maximum absolute error as half the smallest scale division, then divide by the true value and multiply by one hundred per cent.Tutor Registration →
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