You measure the mass of a physics textbook to be 3.80±0.04kg, and use this value to estimate the total mass of exactly 800 identical physics textbooks in the bookstore. What is the absolute uncertainty in your estimate of the total mass a)What is the relative uncertainty in your estimate of the total mass?  b)What is the relative uncertainty in your original measurement of the mass of a single book ?

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b) Since the mass of physics book is expressed as `m^*=3.8pm0.04"kg"`  the absolute error is  `Deltam=0.04"kg."`

The relative uncertainty (error) is ratio of absolute error and absolute value of certain value which is in your case

` ` `deltam=0.04/3.8approx0.010526`

a) Here we first need to calculate the total mass of 800 books which is `800cdot(3.8pm0.04)=3040pm32"kg"`


which is the same as in previous case which is to be expected because we multiplied both error and measured value with the same number. So relative error is the same even though absolute error is much greater.

In real life we wouldn't calculate the mass in such way. We would measure the mass of all 800 books or at least several books at once. 

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