At the end of the calculation round your number to

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Unformatted text preview: three sides of unequal lengths, P = X + Y + Z. Under these conditions, Eq* gives: σP = σ2 + σ2 + σ2 X Y Z How error propagates for additive variables Eq* σQ = N ȹ ∂Q ȹ ∑ ȹ ȹ i =1ȹ ∂X i 2 ȹ σ 2 ȹ Xi Ⱥ X j IV. Propagation of Error Example 2 Consider the case of molar density, ρ = m /(MV) where m = mass, M = molecular weight, and V is volume. Under these conditions, Eq* gives: 2 σρ 2 ȹ σ ȹ ȹ σ ȹ ȹ σ ȹ = ȹ m ȹ + ȹ M ȹ + ȹ V ȹ ρ ȹ m Ⱥ ȹ M Ⱥ ȹ V Ⱥ 2 How error propagates for multiplication and division Eq* σQ = N ȹ ∂Q ȹ ∑ ȹ ȹ i =1ȹ ∂X i 2 ȹ σ 2 ȹ Xi Ⱥ X j V. Significant Figures 1)  When adding or subtracting two numbers, the absolute precision (standard deviation) of the least precise number controls the precision of the final answer. 2)  When multiplying or dividing numbers, the variable with the largest relative error (standard deviation/mean value) will limit the number of significant figures. This rule generally means the final answer will have the same number of significant figures as the error source with the largest relative error. 3)  In principle Eq* will serve to define the number of significant figures during the semester. 4) While...
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This note was uploaded on 01/26/2014 for the course CHEM 3625 taught by Professor Mrjohnson during the Spring '08 term at Virginia Tech.

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