Uncertainties & error propagation
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Flip to reveal answersWhat is the absolute uncertainty of a measurement?
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All 11 Flashcards — Uncertainties & error propagation
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Question
What is the absolute uncertainty of a measurement?
Answer
A ± amount in the **same unit** as the measurement (e.g. 12.4 ± 0.2 cm → Δx = 0.2 cm).
Question
How do you find the fractional uncertainty?
Answer
**Absolute uncertainty ÷ the value** — a plain number with no unit (Δx/x).
Question
How do you get the percentage uncertainty?
Answer
**Fractional × 100%** = (Δx/x) × 100%.
Question
Absolute uncertainty from an instrument's resolution?
Answer
**± half the smallest scale division** (a mm ruler → ±0.5 mm; a 0.01 g balance → ±0.005 g).
Question
Absolute uncertainty from a spread of repeated readings?
Answer
**± half the range** = ½ × (largest − smallest reading).
Question
Propagation rule for + and − (adding/subtracting)?
Answer
**Add the ABSOLUTE uncertainties:** Δy = Δa + Δb.
Question
Propagation rule for × and ÷ (multiplying/dividing)?
Answer
**Add the FRACTIONAL (or %) uncertainties:** Δy/y = Δa/a + Δb/b + Δc/c. (Given in the data booklet.)
Question
Propagation rule for a power, y = aⁿ?
Answer
**Multiply the fractional uncertainty by |n|:** Δy/y = |n·Δa/a|. (Given in the data booklet.)
Question
How do you convert a fractional uncertainty back to an absolute one?
Answer
**Multiply by the value:** Δy = (Δy/y) × y.
Question
How should you round a value and its uncertainty?
Answer
Round the **uncertainty to 1 s.f.**, then round the **value to the same decimal place** (e.g. 2.643 ± 0.087 → 2.64 ± 0.09).
Question
Which uncertainty form do you work in for a × / ÷ / power step?
Answer
**Fractional or percentage** — then convert back to absolute at the end.
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Full study notes for Uncertainties & error propagation
Topic 6.1 hub
Experimental skills
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