error propagation

Question

Q = A B where A = (5.0 ± 0.2) and B = (2.00 ± 0.05). Fractional error in Q is:

RankGuru · Accepted Answer

Rule for multiplication/division: The relative (fractional) error of the result is the sum of the relative errors of the components.
$\frac{\Delta Q}{Q} = \frac{\Delta A}{A} + \frac{\Delta B}{B}$
1. $\frac{\Delta A}{A} = \frac{0.2}{5.0} = 0.04$
2. $\frac{\Delta B}{B} = \frac{0.05}{2.00} = 0.025$
3. **Total Fractional Error**: $0.04 + 0.025 = 0.065$ (or $6.5\%$).

Rank Guru

error propagation

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