Significant Fiqures in Algebraic Operations - Addition, Subtraction , Multiplication , Division - Param Himalaya
1. Addition or Subtraction operation:
The sum of the quantities or difference between the quantities, the final result should retain the least decimal place as in the various numerical values.
Example :
12.32 + 100.004 = 112.324 = 112.32 ( after rounding off upto significant fiqures)
84.0 + 72.24 = 156.24 = 156.2
52.8 + 46.35 = 99.15 = 99.2
9.742-6.02 = 3.722 = 3.72
Question : A box is 2.3 Kg . Two coins of masses 20.15 g and 20.17 g are added to the box .
(a) What is the total mass of the box.
(b) What is the difference in the masses of the coins to correct significant fiqures.
Solution :
Total mass of box = 2.3 Kg + 0.02015 Kg + 0.02017 Kg = 2.34032 = 2.3 Kg round off upto.
Difference = 20.17 - 20.15 = 0.02000 g ( 4 significant fiqures)
2. Multiplication or Division :
In multiplication or division of the numerical values, the final result should retain the least significant.
Example :
(i) X = 4.192 and Y = 2.02
XY = 4.193 × 2.02 = 8.46784
2.02 contains the minimum significant fiqures equal to three , so after rouning off
XY = 8.47
Example: 12.50×169.1 = 2113.75
Each digit is having 4 significant digits.
Therefore, the final answer is rounded off such that it has only 4 significant digits in it
i.e. 2114 will be the answer.
(ii) X = 7500 , Y = 20.83
X/Y = 7500/20.83 = 360.0576
7500 contains the minimum significant fiqures equal to 2 , so the final result can have only two significant fiqures
X/Y = 360