For operations with uncertainty, we’ll follow two different rules depending on whether we're adding/subtracting or multiplying/dividing:
- When measurements are added or subtracted, sum the absolute or relative uncertainty—the result is the same.
- When measurements are multiplied or divided, sum the relative uncertainties.
So anytime you square a measurement, add the uncertainty twice.
To convert between absolute uncertainty and percent uncertainty, we’ll use this formula (m = measurement, Δu = absolute uncertainty):
This problem gives us the maximum and minimum values for the length of a cubit. For parts (a) and (b) of the problem, we just need to convert the units from centimeters to meters, write our equation, and plug in the max and min. Part (c) is a little more complicated: we’ll need the rule for multiplying measurements with uncertainty.
We’ll assume that we know the length and diameter of the cylinder to 0.1 cubit—that is, h = 9.0 cubits and d = 2.0 cubits.
(a) For this part, we just multiply h = 9.0 cubits by the minimum and maximum length of a cubit:￼