Uncertainty, Precision and Significant Figures in a Measurement · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reporting measurements with uncertainty

Science · Scientific Inquiry · ages 16-17
Name ______________________   Date ____________

  1. How should 24.638 cm be reported with a stated absolute uncertainty of 0.2 cm?

    • 24.6 ± 0.2 cm
    • 24.638 ± 0.2 cm
    • 25 ± 0.2 cm

  2. Readings agree closely but lie far from a checked reference value. How should they be described?

    • Accurate but not precise
    • Precise but not accurate
    • Both accurate and precise

  3. Averaging more independent, unbiased readings under stable conditions can reduce the random uncertainty of the mean.

    Circle one:   True   False

  4. An empty balance repeatedly shows 0.5 g instead of zero. What addresses this zero offset?

    • Reset zero or apply a checked correction
    • Average more readings without correction
    • Keep the offset and add display digits

  5. A length is 20.0 ± 0.2 cm. What is its percentage uncertainty?

    Answer: ______________

  6. For basic significant-figure rounding of a product of measured values, use the fewest input figures. Exact counts and defined conversion factors do not limit the count.

    Circle one:   True   False

  7. Hand timing has about 0.2 s reaction uncertainty, while the stopwatch displays 0.01 s steps. Which change addresses the main uncertainty source?

    • Keep hand timing and add display digits
    • Keep hand timing and round more tightly
    • Use electronic start and stop detection

  8. A sum uses A = 20.0 cm with 1% uncertainty and B = 10.0 cm with 0.1% uncertainty. Which input contributes the larger absolute uncertainty?

    • B: its contribution is 0.01 cm
    • A: its contribution is 0.20 cm
    • Both: each contributes 0.10 cm
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reporting measurements with uncertainty W1-mt_HPc3OahYoV-s1

  1. 24.6 ± 0.2 cm · The uncertainty is in tenths of a centimetre, so round the value to tenths.
  2. Precise but not accurate · Their close agreement shows precision. Their distance from the reference shows poor accuracy.
  3. True · Suitable averaging can reduce uncertainty in the mean. It does not shrink individual-reading scatter or remove a shared offset.
  4. Reset zero or apply a checked correction · The known empty-balance reference reveals a zero offset. Resetting or a documented correction addresses that offset.
  5. 1 · (0.2 ÷ 20.0) × 100% = 1%.
  6. True · This is the basic product-rounding rule, with exact quantities excluded from the limiting count.
  7. Use electronic start and stop detection · Reaction uncertainty is larger than the display step. Electronic detection addresses the timing method rather than adding digits.
  8. A: its contribution is 0.20 cm · A contributes 20.0 × 0.01 = 0.20 cm. B contributes 10.0 × 0.001 = 0.01 cm. A is larger.
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