Combining Uncertainties and Reading a Result off a Graph · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Honest numbers with error bars

Science · Scientific Inquiry · ages 17-18
Name ______________________   Date ____________

  1. Lengths 5.0 plus or minus 0.1 and 3.0 plus or minus 0.2 are added. What is the absolute uncertainty of the total?

    • 0.1
    • 0.2
    • 0.3

  2. A scale reads nearly the same each time but far from the true value. What is it?

    • Precise but not accurate
    • Accurate but not precise
    • Neither accurate nor precise

  3. A result quoted with no stated uncertainty is unfinished. True or false?

    Circle one:   True   False

  4. How do the best line and the worst acceptable lines give a gradient uncertainty?

    • The sum of the two slopes
    • Half the spread between them
    • The steeper slope alone

  5. One input of a product has 1 percent uncertainty and another has 8 percent. Which limits the result most?

    • The smallest input
    • The average of the inputs
    • The one with the largest fractional error

  6. One value has 4 percent uncertainty and another has 6 percent. They are multiplied. Give the combined percent uncertainty.

    Answer: ______________

  7. All inputs have two significant figures. How should you quote the answer?

    • With as many digits as shown
    • With two significant figures
    • With six significant figures

  8. Two labs report 10.0 plus or minus 0.2 and 10.3 plus or minus 0.2. Do the values agree?

    • They disagree
    • They agree
    • Nothing can be said
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Answer key

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

Honest numbers with error bars W1-mt_kn8RhTDEOK-s1

  1. 0.3 · For sums the absolute errors add: 0.1 plus 0.2 is 0.3.
  2. Precise but not accurate · Matching repeats mean precision, while distance from truth means poor accuracy.
  3. True · Quoting plus or minus honestly is the first lab skill.
  4. Half the spread between them · Half the spread between steepest and shallowest is the gradient uncertainty.
  5. The one with the largest fractional error · The largest fractional error dominates the final spread.
  6. 10 · For products the fractional errors add: 4 plus 6 is 10 percent.
  7. With two significant figures · Rounding matches the weakest input instead of inventing certainty.
  8. They agree · The gap of 0.3 fits inside the combined 0.4, so they agree.
Worksheet · LightMySky