Suppose your bathroom scale reads your mass as 65 kilograms with a three percent uncertainty. What is the uncertainty in your mass in kilograms?
We can refer to the uncertainty in our mass in kilograms as capital 𝑈 with a scale reading of 65 kilograms. And knowing that there’s a three percent uncertainty, we can say that the uncertainty in our mass in kilograms equals our given mass by the scale multiplied by the uncertainty factor, three percent.
As a decimal, three percent equals 0.03. And when we multiply these two numbers together, we find that to one significant figure the uncertainty in our mass is two kilograms. That’s the value above and below the scale reading that we may in fact have.