Worked example
For this exercise, 10.0 ± 0.2 cm means an interval from reading minus 0.2 to reading plus 0.2. What is that interval?
Answer & why
Answer: 9.8 to 10.2 cm
10.0 − 0.2 = 9.8 and 10.0 + 0.2 = 10.2.
Grade 12 · Science
Interpret measurement uncertainty
Use explicitly defined uncertainty intervals to report measurements without claiming more precision than the method supports.
6 authored questions + worked example
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All questions
All 6 authored questions for this skill.
Question 1
A method reports length only to the nearest millimeter. Which report avoids unsupported extra decimal precision?
- 24.0000000 mm
- 24.000000 mm
- 24 mm
- 24.00000000 mm
A hint
Use the stated meaning of ± in this exercise; overlapping intervals alone do not prove equality or a difference.
Answer & why
Answer: 24 mm
The method does not support additional decimal places.
Question 2
Repeated measurements are tightly grouped around a value known to be wrong because of a zero-offset error. What problem remains?
- No possible error because repeats agree.
- A systematic measurement bias.
- A change in the unit's name.
- A guarantee of perfect accuracy.
A hint
Use the stated meaning of ± in this exercise; overlapping intervals alone do not prove equality or a difference.
Answer & why
Answer: A systematic measurement bias.
Agreement among repeats does not remove a shared calibration offset.
Question 3
Two measured intervals overlap. Which conclusion is justified from overlap alone?
- Overlap alone does not prove the underlying values are exactly equal.
- Both measurements must be fake.
- Every possible difference is proved.
- The underlying values must be identical.
A hint
Use the stated meaning of ± in this exercise; overlapping intervals alone do not prove equality or a difference.
Answer & why
Answer: Overlap alone does not prove the underlying values are exactly equal.
Interpretation depends on the uncertainty model and evidence; overlap is not an equality proof.
Question 4
A balance consistently reads 2 g too high on a known reference. What should be addressed?
- Whether all high readings should be deleted without explanation.
- The reference's printed color.
- Its calibration or zero offset.
- Only the number of digits in its brand.
A hint
Use the stated meaning of ± in this exercise; overlapping intervals alone do not prove equality or a difference.
Answer & why
Answer: Its calibration or zero offset.
A consistent offset calls for calibration and transparent correction, not selective removal.
Question 5
For this exercise, 10.0 ± 0.2 cm means an interval from reading minus 0.2 to reading plus 0.2. What is that interval?
- 9.8 to 10.2 cm
- 0.2 to 10.0 cm
- 8.0 to 12.0 cm
- 10.0 to 10.2 cm
A hint
Use the stated meaning of ± in this exercise; overlapping intervals alone do not prove equality or a difference.
Answer & why
Answer: 9.8 to 10.2 cm
10.0 − 0.2 = 9.8 and 10.0 + 0.2 = 10.2.
Question 6
Using the same interval convention, 5.0 ± 0.1 g and 5.2 ± 0.1 g share which endpoint?
- 5.3 g
- 4.8 g
- 5.0 g
- 5.1 g
A hint
Use the stated meaning of ± in this exercise; overlapping intervals alone do not prove equality or a difference.
Answer & why
Answer: 5.1 g
Their intervals are 4.9–5.1 g and 5.1–5.3 g.