Errors in Sums and Differences
If z = a x plus or minus b y with exact coefficients and bounded input uncertainties, the maximum absolute uncertainty is Delta z = |a|Delta x + |b|Delta y to first order.
Why this shows up in the exam
Finding thickness by subtraction · Combining measured lengths · Uncertainty budgets for offsets
Learn the idea
For worst-case independent bounds, absolute uncertainties add when measured quantities are added or subtracted. Subtraction does not subtract ignorance: uncertain endpoints can shift in opposite directions and enlarge the uncertainty of their difference.
🧠 Memory hook: Values may subtract; worst-case absolute errors add.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta(x+y) = Delta x + Delta y — maximum absolute error in a sum
- Delta(x-y) = Delta x + Delta y — maximum absolute error in a difference
- Delta z = sum |a_i| Delta x_i — linear combination with exact coefficients
How to approach it
- 1Write the output expression
- 2Use absolute errors for additive terms
- 3Add coefficient-weighted uncertainty magnitudes
Common slip-ups that cost marks
- •Subtracting uncertainty in a difference
- •Adding percentage errors for a simple sum
- •Ignoring exact numerical coefficients
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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