Rules for uncertainty

Rules for finding uncertainties in different situtations, and combining uncertainties. And definitions.

What is the uncertainty in a reading?

± half the smallest division e.g. uncertainty in the temperature of an analog thermometer measured to 1C would be ±0.5C

• What’s the uncertainty in a measurement

(at least) ±1 smallest division

What’s the uncertainty in repeated data

half the range i.e. ± ½ (largest - smallest value)

What’s the uncertainty in digital readings?

± the last significant digit (unless otherwise quoted)

How do you add/subtract data with uncertainties?

add the absolute uncertainty

How do you multiply or divide data with uncertainties?

add percentage uncertainty

How do you raise data with uncertainties to a power?

multiply percentage uncertainty by the power

How do you multiply data with an uncertainty by a constant?

multiply the absolute uncertainty by the constant

How to find the percentage uncertainty from a graph.

(best fit - worst fit)/best fit

i.e. line of best fit/line of worst fit

What is the uncertainty when only a single number is given?

+- 1 of the last significant digit. Additionally, the power/unit carries over. E.g: 3.5×10³ = +-0.1×10³