# Combining Uncertainties - Multiplying and Dividing

So far, we have dealt only in absolute uncertainties - uncertainties that can be measured in the units our measured value is in. For example, someone's height could be 180 cm with an absolute uncertainty of ± 10cm.

When we have to combine uncertainties by multiplying or dividing data, we must use percentage uncertainties as well. Here's how it works:

Let’s say we have to combine the uncertainties on voltage and current measurements to work out the resistance of a light bulb in a circuit. We would be using Ohm’s Law, V = IR. Rearranging for R we have R = V/I. So, after getting readings for the voltage, V, and current, I, we must divide them. What happens to their associated uncertainties? Let's find out.

Say the voltage is 5.2 ± 0.1 V and the current is 0.84 ± 0.05 A.

We do this by using the formula: uncertainty/value x 100

For voltage: 0.1/5.2 x 100 = 1.92 ~ 2%

For current: 0.05/0.84 x 100 = 5.95 ~ 6%

The next step is to do the calculation for resistance: R = V/I

R = 5.20 / 0.84 = 6.19 Ω

Next is combining the percentage uncertainties. To do that, we simply add them:

2% + 6% = 8%

And finally, we must convert the percentage uncertainty back to an absolute uncertainty:

8/100 x 6.19 = 0.5 Ω

Rounding our resistance value to account for the uncertainty, this gives our answer for resistance to be:

R = 6.2 ± 0.5 Ω