- #1

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the uncertainty in the final result would be?

Do I just add up the uncertainty to get the final uncertainty?

What if I was aked to multiply them?

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- Thread starter UrbanXrisis
- Start date

- #1

- 1,197

- 1

the uncertainty in the final result would be?

Do I just add up the uncertainty to get the final uncertainty?

What if I was aked to multiply them?

- #2

HallsofIvy

Science Advisor

Homework Helper

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Similarly, 6.8+/- 0.4 cm could be as low as 6.8- 0.4= 6.4 cm or as high as 6.8+0.4= 7.2 cm.

Suppose you added those two largest values? Do you see that adding any other possible values would be less than that? Suppose you added the smallest values. Do you see that adding any other possible values would be more than that? What is the range of possible sums?

Actually you are correct that you can just add the "uncertainties".

If one is "a+/- x" and the other "b+/- y", then the largest the first number can be is a+x and the largest the second number can be is b+y. Adding those, we get a+ x+ b+ y= (a+b)+ (x+y) as the largest possible sum. The smallest the first number can be is a-x and the smallest the second number can be is b- y. Adding those, we get a-x+ b- y= (a+b)- (x+y). In other words, all possible sums lie between (a+b)-(x+y) and (a+b)+(x+y) which we can write as (a+b) +/- (x+y). The uncertainty of the sum is the sum of the uncertainties.

Multiplying is more complicated. Taking the same situation as above, (a+x)(b+y)=

ab+ bx+ay+ xy and (a-x)(b-y)= ab- bx- ay+ xy. Because of the xy term, that

The uncertainty divided by the number itself is called the "relative uncertainty". That's were we get the engineer's "rule of thumb": "If measurements are added, the uncertainties are added. If measurements are multiplied, the relative uncertainties are added". (The term "error" is more often used for your "uncertainty").

That's a "rule of thumb" because it is not exactly true- it's ignoring that "xy" term.

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