How to determine the uncertainty of a measurement?

The uncertainty of a measurement is determined by considering the precision of the measuring instrument and any human error.

In more detail, the uncertainty of a measurement is a range within which the true value of the measurement is likely to lie. It is an estimate of the level of confidence that a scientist has in the results of a measurement. There are two types of uncertainties that can affect a measurement: systematic and random.

Systematic uncertainties are consistent, predictable errors that are usually caused by the measuring instrument. For example, if a ruler is slightly bent or a stopwatch is consistently slow, these would cause systematic uncertainties. These can often be corrected for by calibrating the instrument.

Random uncertainties, on the other hand, are unpredictable and arise from factors that are difficult to control, such as human error in reading an instrument or natural fluctuations in the quantity being measured. These can be reduced by taking multiple measurements and calculating an average.

To determine the uncertainty of a measurement, you first need to identify the precision of the measuring instrument. This is usually given by the smallest division on the scale of the instrument. For example, if you are using a ruler with millimetre divisions, the precision of your measurement is ±0.5 mm.

Next, consider any potential sources of human error. This could be uncertainty in reading the scale of the instrument, or in how consistently you are able to make the measurement. For example, if you are timing an event with a stopwatch, there may be uncertainty in your reaction time in starting and stopping the watch.

Finally, if you are taking multiple measurements, you can calculate the standard deviation of your results. This gives a measure of how spread out your measurements are, and can be used as an estimate of the uncertainty.

Remember, it's important to always report your measurements with their associated uncertainties, to give a complete picture of the reliability of your results.