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, Δ*u *= absolute uncertainty):

$\overline{){m}{\pm}{\u2206}{u}{=}{m}{\pm}\left(\frac{\u2206u}{m}\times 100\%\right)}$

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:￼

${h}_{min}=9(43\mathrm{cm})\left(\frac{{10}^{-2}\mathrm{m}}{1\mathrm{cm}}\right)=9(0.43\mathrm{m})=\mathbf{3}\mathbf{.}\mathbf{87}\mathbf{}\mathbf{m}$ and ${h}_{max}=9(53\mathrm{cm})\left(\frac{{10}^{-2}\mathrm{m}}{1\mathrm{cm}}\right)=9(0.53\mathrm{m})=\mathbf{4}\mathbf{.}\mathbf{87}\mathbf{}\mathbf{m}$