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Significant figures 

As physics is based on measurements. But unfortunately whenever a physical quantity is measured, there is inevitably some uncertainty about its determined value. This uncertainty may be due to a number of reasons. One reason is the type of instrument, is being used. We know that every measuring instrument is calibrated to a certain smallest division and this fact put a limit to the degree of accuracy which may be achieved while measuring with it. Suppose that we want to measure the length of a straight line with the help of a meter rod calibrated in millimeters. Let the end point of the line does not touch or cross the midpoint of the smallest division, the reading is confined to the previous division. In case the end of the line seems to be touching or have crossed the midpoint, the reading is extended to the next division. By applying the above rule the position of the edge of a line recorded as 12.7 cm, with the help of a meter rod calibrated 1 millimeters may lie between 12.65 cm. and 12.75 cm, thus in this example the maximum uncertainty is ± 0.05 cm. it is, in fact, equivalent to an uncertainty of 0.1 cm equal to the least count of the instrument divided into two parts, half above and half below the recorded reading. The uncertainty or accuracy in the value of a measured quantity can be indicated conveniently by using significant figures. The recorded value of the length of the straight line i.e. 12.7 cm contains three digits (1,2,7) out of which two digits (1& 2) are accurately known while the third digits i.e. 7 is a doubtful one. As a rule:




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