Units and Measurement

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Significant figures in the measured value of a physical quantity tell the number of digits in which we have confidence. Larger the number of significant figures obtained in a measurement, greater is the accuracy of the measurement. The reverse is also true.

The following rules are observed in counting the number of significant figures in a given measured quantity.
(1)  All non-zero digits are significant.
Example :
42.3 has three significant figures.
243.4 has four significant figures.

(2)  A zero becomes significant figure if it appears between to non-zero digits.
Example:
5.03 has three significant figures.
5.604 has four significant figures.

(3)  Leading zeros or the zeros placed to the left of the number are never significant.
Example:
0.543 has three significant figures.
0.045 has two significant figures.

(4) Trailing zeros or the zeros placed to the right of the number is significant.
Example:
4.330 has four significant figures.
433.00 has five significant figures.

(5) In exponential notation, the numerical portion gives the number of significant figures.
Example:
1.32 x 10–2 has three significant figures.
1.32 x 104 has three significant figures.

The rule by convention is that the preceding digit is raised by 1 if the insignificant digit to be dropped (the underlined digit in this case) is more than 5, and is left unchanged if the latter is less than 5.

But what if the number is 2.745 in which the insignificant digit is 5. Here, the convention is that if the preceding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceding digit is raised by 1. Then, the number 2.745 rounded off to three significant figures becomes 2.74

Following rules for arithmetic operations with significant figures:

In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.

In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal place.

If a set of experimental data is specified to n significant figures, a result obtained by combining the data will also be valid to n significant figures.