What is an error?

As we have seen in an earlier post, a physical quantity is a property of an object that can be measured with a measuring instrument.  Hence when you use a measuring instrument you would obtain a reading. The reading is simply a numerical value that you can read off a measuring instrument such as the volume off a measuring cylinder or the time off a stopwatch.

We must also introduce what is called the true value. The true value is the reading that you would obtain if the measurement is done in ideal conditions.

In order to obtain the the true value the following conditions must be present:

1. You must have the skills to use the instrument and know the steps that must be followed to obtain the reading.
2. You must be using instruments that are properly calibrated and are not damaged.
3. All the conditions that are required to obtain the true value must be present. For example 1/3 of the stem of the thermometer must be immersed in the liquid, the pressure must be one bar, the liquid used in the measuring cylinder must have a temperature of 20⁰C.
4. If a calculation is needed to determine the magnitude of a physical quantity, then the correct equation and the right constant must be used.

Now an error is made when the reading that you obtain is not equal to the true value.  And the magnitude of the error is the difference between the reading obtained and the true value.

Then we can thus introduce the term accuracy and precision.

A measurement is accurate if it is close to the true value. And if there are two values then the one that is closest to the true value is the most accurate.

The precision of an instrument is the smallest value that can be measured using the instrument. Hence if a length is measured using a metre rule then it is precise to 1 mm or it has a precision of 1 mm. However a length that is measure using a vernier caliper has a precision of 0.1 mm. Hence the length that is measure using a vernier caliper is most precise.