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## Uncertainties in measurements

Every measurement has an uncertainty. There are several methods we can use to determine the uncertainty in a measurement.

## Half smallest division rule

Use this rule when the greatest source of your uncertainty is from your equipment.

(For example when using a ruler, multimeter, or a scale)

(For example when using a ruler, multimeter, or a scale)

**"For a single measurement, the absolute uncertainty is half of the smallest scale division"**

__Example:__

If we were to measure the temperature on an ordinary thermometer that is marked at every 1°C, the uncertainty in our measurement would be 0.5°C. Therefore if we measured the temperature to be 13°C, we would express this value with it's absolute uncertainty as:

Length = (13.0 ± 0.5) °C

## Half range rule

Use this rule when the greatest source of uncertainty is not from your equipment.

(for example when using stop watch and user reaction time is the greatest source of uncertainty)

(for example when using stop watch and user reaction time is the greatest source of uncertainty)

**"If there are multiple measurements, the absolute uncertainty is half of the range of the measurements"**

__Example:__

The amount of time taken for a pendulum to swing back and forth is recorded multiple times. The times recorded are...

1.42s, 1.37s, 1.40s, 1.42s, 1.40s, 1.39s, 1.37s

The range of these measurements is: 1.42s - 1.37s = 0.05s

The absolute uncertainty is half of this: (0.05s)/2 = 0.025s = 0.03s (1sf)

The average of these measurements is 1.396s = 1.40s (rounding to 2dp, the same as the uncertainty)

Our complete value with absolute uncertainty is:

The absolute uncertainty is half of this: (0.05s)/2 = 0.025s = 0.03s (1sf)

The average of these measurements is 1.396s = 1.40s (rounding to 2dp, the same as the uncertainty)

Our complete value with absolute uncertainty is:

Time = 1.40 ± 0.03s