propagation of errors (product)

Question

If A = (2.00 ± 0.02) and B = (3.0 ± 0.1), relative error in product P = AB is approximately?

RankGuru · Accepted Answer

1. **Rule for Product Errors**: For $P = AB$, the relative error in the product is the sum of the relative errors in the components: $\frac{\Delta P}{P} = \frac{\Delta A}{A} + \frac{\Delta B}{B}$.
2. **Relative error in A**: $\frac{0.02}{2.00} = 0.01$ (or $1\%$).
3. **Relative error in B**: $\frac{0.1}{3.0} \approx 0.0333$ (or $3.33\%$).
4. **Total Relative Error**: $0.01 + 0.0333 = 0.0433$.
5. **Percentage conversion**: $0.0433 	imes 100\% \approx 4.3\%$.
6. **Conclusion**: The closest estimate is **$4\%$**.

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propagation of errors (product)

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