# Absolute and Percentage Uncertainties

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#1
Example: If I am given the equation, a = 2b + c, will all three variables be of the same units, if I'm asked to find the absolute uncertainty in "a"? And, do all three variables have to be of the same unit, if asked to find the percentage uncertainty in "a" instead?
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5 months ago
#2
(Original post by Dracorius)
Example: If I am given the equation, a = 2b + c, will all three variables be of the same units, if I'm asked to find the absolute uncertainty in "a"? And, do all three variables have to be of the same unit, if asked to find the percentage uncertainty in "a" instead?
a, b and c must all be in the same units if you add them.

The absolute uncertainty in a will be the sum of the 2 x absolute uncertainty in b plus the uncertainty in c.

The % uncertainty in a is then just calculated as usual for any % uncertainty value taking that total uncertainty you just found as a % of the final value.
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#3
(Original post by Stonebridge)
a, b and c must all be in the same units if you add them.

The absolute uncertainty in a will be the sum of the 2 x absolute uncertainty in b plus the uncertainty in c.

The % uncertainty in a is then just calculated as usual for any % uncertainty value taking that total uncertainty you just found as a % of the final value.
okay, what happens if the equation is a = b^2 + c? would the absolute uncertainty for a be the % uncertainty in b squared plus the % uncertainty in c?
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5 months ago
#4
(Original post by Dracorius)
okay, what happens if the equation is a = b^2 + c? would the absolute uncertainty for a be the % uncertainty in b squared plus the % uncertainty in c?
In this case, the units of b2 would have to be the same as the unit of c.

You do this by first finding the absolute uncertainty in b2 and adding it to the absolute uncertainty in c
To find the absolute uncertainty in b2, you first find the % uncertainty in b and multiply by 2.
Then convert that % uncertainty back to an absolute uncertainty in b2 before adding it, as said, to the absolute uncertainty in c.
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