(ii)In multiplying or dividing numbers, keep a number of significant figures in the product or quotient not more than that contained in the least accurate factor i.e., the factor containing the least number of significant figures. For example, the computation of the following using a calculator, gives
As the factor , the least accurate in the above calculation has three significant figures, the answer should be written to three significant figures only. The other figures are insignificant and should be deleted. While deleting the figures, the last significant figure to be retained is rounded off for which the following rules are followed.
a) If the first digit dropped is less than 5, the last digit retained should remain unchanged.
b) If the first digit dropped is more than 5, the digit to be retained is increased by one.
c) If the digit to be dropped is 5, the previous digit which is to be retained is increased by one if it is odd and retained as such if it is even. For example, the following numbers are rounded off to three significant figures as follows. The digits are deleted one by one.
43.75 is rounded off as 43.8
56.8546 is rounded of as 56.8
73.650 is rounded off as 73.6
64.350 is rounded off as 64.4
Following this rule, the correct answer of the computation given is section (ii) is .
(iii) In adding or subtracting numbers, the number of decimal places retained in the answer should equal the smallest number of decimal places in any of the quantities being added or subtracted. In this case, the number of significant figures is not important. It is the position of decimal that matters. For example, suppose we wish to add the following quantities expressed in meters
i) 72.1
ii) 2.7543
3.42 4.10
Correct answer: 75.5 m 8.13 m
In case (i) the number 72.1 has the smallest number of decimal places, thus the answer is rounded off to the same position which is then 75.5m. in case (ii), the number 4.10 has the smallest number of decimal places and hence, the answer is rounded off to the same decimal positions which is then 8.13m.