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S3 Maths: Significant Figures and Percentage Error (Paper 4 (error clinic))
S3 Maths: Significant Figures and Percentage Error (Paper 4 (error clinic))
Paper 4 (error clinic): ten questions on significant figures and percentage error, with answers and one line notes.
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 0.00203 have?
- FoundationHow many significant figures does 5.0 have?
- FoundationRound 0.0458 to two significant figures.
- IntermediateHow is the maximum absolute error related to the smallest scale division?
- IntermediateDoes percentage error have a unit? What about relative error?
- IntermediateWork out 4.7 minus 1.2, keeping one decimal place.
- ChallengeA quantity rounded to the nearest 100 is written as 1000. What is the maximum absolute error?
- ChallengeIs percentage error the absolute error divided by the true value or by the measured value?
- ChallengeA bag of salt has a true mass of 250 g and a maximum absolute error of 5 g. Find the percentage error.
- Error redoError clinic: a length measures 6.8 cm to the nearest 0.1 cm and a student writes a maximum absolute error of 0.1 cm. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Three | The three leading zeros do not count, so 2, 0 and 3 give three significant figures. |
| 2 | Two | The zero after the decimal point counts, so 5 and 0 give two significant figures. |
| 3 | 0.046 | The first two significant figures are 4 and 5, and the next digit 8 rounds the 5 up to 6. |
| 4 | It equals half of the smallest division | The measurement is rounded to the nearest division, so the true value is at most half a division away. |
| 5 | Percentage error is a percentage and relative error has no unit | Relative error is a ratio of two like quantities so units cancel, and percentage error is that ratio multiplied by one hundred. |
| 6 | 3.5 | Both numbers have one decimal place, so subtracting gives 3.5. |
| 7 | 50 | The smallest division is 100 and half of that is 50. |
| 8 | By the true value | By definition percentage error is the absolute error divided by the true value, times one hundred per cent. |
| 9 | 2% | Five divided by 250 times one hundred per cent gives 2 per cent. |
| 10 | 0.05 cm | The maximum absolute error is half the smallest division, 0.1 divided by 2, not a whole division. |
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 →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
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