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Estimate the absolute and relative standard deviations of the following calculations. The number in parentheses is the standard deviation of the preceding value.

a) z=5.64(s=0.14)*log(138)(s=3)

2. Homework Equations

Sx/x =SQRT((Sp/P)2+(Sq/q)2+(Sr/R)2

Sx=0.434(Sp/P)

3. The Attempt at a Solution

I thought of two ways to go about the problem I am not sure which way is correct here are both attempts:

log(138)= 2.139

Z=12.069

SZ=SQRT((0.14/5.64)2+(3.0/2.139)2)=1.40

Z=12.07 LaTeX Code: \\pm 1.40

RSD=(1.4/12.07)*100 =11.6%

Or my other attempt:

Z=12.07

(0.14/5.64)2+(0.434*(3.0/138))=0.01

Z=12.07LaTeX Code: \\pm 0.01

RSD=(0.01/12.07)*100=0.08%

Are either of these ways correct? Any help would be appreciated. Thanks.