Propagating Uncertainty Through a Calculation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

How uncertainty travels through your math

Science · Chemistry · ages 18-19
Name ______________________   Date ____________
  1. You work out the refraction index from angle readings that each wobble a little. What happens to that wobble?

    • It moves through the formula into the calculated index
    • It stays behind in the angles
    • It cancels itself out in the math
  2. You add two measured lengths. How do you combine their uncertainties?

    • Add their percentage wobbles
    • Add their absolute ranges
    • Multiply their absolute ranges
  3. One reading is 10.24 and another is 10.11. What is their difference?

    Answer: ______________

  4. Each input wobbles by about 0.01, yet 10.24 minus 10.11 carries a huge percentage wobble. Why?

    • The answer 0.13 is tiny next to the wobble of the inputs
    • The inputs were rounded to too few digits
    • Subtraction always doubles every input wobble
  5. A value wobbles by 2 percent and you square it. About what wobble does the square carry?

    • About 1 percent
    • About 2 percent
    • About 4 percent
  6. A length measured to three digits lets you quote a result calculated from it to ten digits.

    Circle one:   True   False

  7. A student adds two masses and combines their percentage wobbles. What is the mistake?

    • The units of mass forbid adding the two values
    • Averaging the masses would remove all wobble
    • A sum needs absolute ranges, not percentage wobbles
  8. Your angles wobble by two degrees and your distances are nearly exact. You want a tighter refraction index. What do you improve first?

    • The distances, because exact numbers are suspicious
    • The angle readings, because their wobble moves the answer most
    • Both equally, because every input matters the same
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Answer key

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

How uncertainty travels through your math W1-mt_xssxg6NqQM-s1

  1. It moves through the formula into the calculated index · Ranges never disappear in a formula. They travel into the result.
  2. Add their absolute ranges · Sums and differences combine through absolute ranges.
  3. 0.13 · 10.24 minus 10.11 is 0.13.
  4. The answer 0.13 is tiny next to the wobble of the inputs · A small difference between large numbers makes any fixed wobble loom large.
  5. About 4 percent · The exponent multiplies the percentage, and two times 2 is 4.
  6. False · The answer must stop where the least precise input stops.
  7. A sum needs absolute ranges, not percentage wobbles · Percentages are the rule for products and quotients, not for a sum.
  8. The angle readings, because their wobble moves the answer most · Effort belongs to the input whose wobble moves the answer most.
Worksheet · LightMySky