What are significant figures?

Most of the students have misunderstanding regarding the significant figures. In physics every measurement has certain number of significant figures. First of all one should know that figure in this context is digit. In simple words one can say that significant figure (digit) is that one which is measured with certain reliability. Let us explain it with certain examples.

Let we are given lead pencil and asked to measure its length with ordinary meter rod that has marking up to a millimeter. First of all we will see that reading is less than meter and we are no need to measure that how many meters pencil is long. After that we will measure its length in decimeter that is the tenth part of meter, and we find that it is 1 decimeter (say) and little more. Part of the pencil more than decimeter is measured in centimeter, let say it is 2 centimeter and little more. That little more part of the pencil will be measured in millimeter that may come about 4 millimeter. At the end we quote that the length of pencil in SI unit is 0.124 m. In this measured length there are 3 significant figures, that are 1 decimeter, 2 centimeters, and 4 millimeter. Zero is not significant because we have not taken any measurement in meter as the pencil was too short than meter.

Let us consider measurement of another pencil (say) 0.203 m. This measurement also has three significant figures. In this measurement first “0” is again not significant because length was too short than a meter. “2” decimeter is significant because we have measured it. “0” in between 2 and 3 is significant because we have measured length in centimeter although it was zero. Again “3” is also significant as we have measured the remaining length as 3 milimeter.

In third example of measurement we consider 0.003 m. Most of the student confuse that zeros after the decimal point are significant but they are wrong. Actually this reading was the length was short than decimeter as well as centimeter (say the width of match stick). When we started taking reading in decimeter it was too short, after that we find to measure how many centimeters are there, again it is shorter than centimeter. At the end reading was taken in millimeter which was 3 millimeter. As a result we can say that in this case we have noted reading only in milimeter which was only one figure and our measurement has one significant figure.

While measuring the length of bed, one taken it as 2.100 m. In this measurement there are four significant figures. The reason is that there were 2 meters and little more in the length of bed. Remaining length of the bed was measured in decimeter and was found 1 decimeter. After that it was measured that there are 0 centimeter and 0 millimeter in the measurement. Although readings in centimeter and millimeter were zero but they were measured with scale that can measure upto millimeter.

Any query regarding this topic is welcomed and will be answered !

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