Accuracy and precision of measuring instruments
All measurements are made with the help of instruments. The accuracy to which a measurement is made depends on several factors. For example, if length is measured using a metre scale which has graduations at 1 mm interval then all readings are good only upto this value. The error in the use of any instrument is normally taken to be half of the smallest division on the scale of the instrument. Such an error is called instrumental error. In the case of a metre scale, this error is about 0.5 mm.
Physical quantities obtained from experimental observation always have some uncertainity. Measurements can never be made with absolute precision. Precision of a number is often indicated by following it with ± symbol and a second number indicating the maximum error likely.
For example, if the length of a steel rod = 56.47 ± 3 mm then the true length is unlikely to be less than 56.44 mm or greater than 56.50 mm. If the error in the measured value is expressed in fraction, it is called fractional error and if expressed in percentage it is called percentage error. For example, a resistor labelled "470 Ω, 10%" probably has a true resistance differing not more than 10% from 470 Ω. So the true value lies between 423 Ω and 517 Ω.