Absolute, Relative, and Percentage Error
For a nonzero measured value x with absolute uncertainty Delta x, the relative uncertainty is Delta x/|x| and the percentage uncertainty is 100 Delta x/|x|; the uncertainty magnitude is reported nonnegative.
Why this shows up in the exam
Comparing instruments at different ranges · Reporting laboratory results · Setting engineering tolerances
Learn the idea
Absolute error has the quantity's unit, while relative and percentage errors compare it with the measured magnitude. An uncertainty of one centimetre matters very differently for a pencil and a highway, so divide by the value before comparing measurement quality.
🧠 Memory hook: Absolute carries units; relative divides; percent multiplies by 100.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- relative error = Delta x/|x| — dimensionless fractional uncertainty
- percentage error = 100 Delta x/|x| — fractional uncertainty expressed as percent
- x = x_m plus or minus Delta x — standard absolute-uncertainty form
How to approach it
- 1Find the stated absolute uncertainty
- 2Divide by the magnitude of the result
- 3Multiply by 100 only if percent is requested
Common slip-ups that cost marks
- •Dividing by the uncertainty instead of the value
- •Attaching units to percentage error
- •Keeping a negative sign on uncertainty magnitude
🌟 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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