Measurements and Readings

When using a tool like a ruler or a meter stick we must line up the zero point, and also read off the value of whatever we are measuring. The fact that we must align the zero point means that tools like this produce measurements.

Since measurements have a ‘zeroing uncertainty’ we must make two judgments. We must factor in the uncertainty associated with resolution two times.

The uncertainty associated with the resolution of a tool is ± half the resolution when aligning the zero point, and ± half the resolution reading off the value, the total uncertainty for a measurement is ± the resolution of the tool.

Remember, the resolution of a device is the smallest interval between divisions.

Readings do not have a ‘zeroing uncertainty’ as devices that produce readings are already zeroed for you by a manufacturer. Because of this, we consider a tool like a digital voltmeter, weighing scales, or thermometers to have no uncertainty associated with their zeroing. This means that uncertainty comes only from the one judgment we make when reading off our value. So, tools with no zeroing uncertainty have an uncertainty of ± half their resolution.