Significant Figures
The significant figures express the accuracy with which the physical quantity may be expressed. They are the digits which give us useful information about the accuracy of the measurement.
Greater the number of significant figures obtained when making a measurement, more accurate is the measurement, conversly, a measurement made to only few significant figure is not a very accurate one. For example, a recorded figure of 5.32 means the quantity can be relied on as accurate to three significant figures and a figure of 5.32 1 is said to be accurate to four significant number.
The following rules have been set up for determining the number of significant figures:
1. All non-zero digits are significant. 243,48 contains five significant figures.
2. All zeros occuring between two nonzero digits are significant. For example, 46.0009 contains six significant figures.
3. All zeros to the right of a decimal point and to the left of a non-zero digit are never significant 0.00678 contains three significant figures. The single zero conventionally placed to the left of the decimal point in such an expression is also never significant.
4.
(a) All zeros to the right of a decimal point are significant if they are not followed by a non-zero digit. For example, 30.00 contains four significant figures.
(b) All zeros to the right of the last non-zero digit after the decimal point are significant. For Example, 0.054300 contains five significant figures.
5.
(a) All zeros to the right of the last (rightmost) non-zero digit are not significant.
Ex. 3030 contains three significant figures.
(b) All zeros to the right of the last non-zero digit are significant if they come from a measurement. Suppose that the distance between two objects is measured to be 3030 m. Then 3030 m contains four significant figures.
6. Change of units does not change the number of significant figures in a measurement.
For example, the length x = 2.308 cm ha four significant digits. In different units, the same length can be written as x = 23.08 mm: x = 0.00002308 km. All these numbers have the same number of significant figures namely four, the digits 2, 3, 0 and 8.
