How do you determine the maximum possible error in a measurement?

The maximum possible error in a measurement is half the smallest unit of measurement used.

When you take a measurement, the precision of your measuring tool determines the smallest unit you can measure. For example, if you are using a ruler marked in millimetres, the smallest unit is 1 millimetre. The maximum possible error is half of this smallest unit because the true value could be up to half a unit more or less than the measured value. So, if your ruler measures to the nearest millimetre, the maximum possible error is 0.5 millimetres.

To understand this better, imagine you measure a length and find it to be 10 millimetres. The actual length could be anywhere from 9.5 millimetres to 10.5 millimetres. This range is due to the limitation of your measuring tool. Therefore, the maximum possible error is ±0.5 millimetres.

This concept applies to any measurement tool. If you are using a digital scale that measures to the nearest gram, the maximum possible error is ±0.5 grams. If a thermometer measures to the nearest degree, the maximum possible error is ±0.5 degrees. Always remember, the maximum possible error is half the smallest unit of measurement, ensuring you account for the precision limits of your measuring instrument.