Significant figures computations and examples

Dr. Walt Volland,   revised July 5, 2012 all rights reserved

Handling significant figures in addition and subtraction follow a different rule than multiplication and division.  The rule for addition and subtraction gives an answer with the same number of decimal places as the quantity with the fewest number of decimal places. EXAMPLE .                                                                                                                                                        What is the sum for the following three quantites  123.0 cm + 3.000 cm + 11.02 cm?                         The total adds to 137.02 cm which needs to be rounded off to one decimal place 137.0 cm where the zero after the decimal point is a significant digit..   EXERCISES 1. When the 3.6 kg is converted to grams what will be the number of significant figures in the result? ANSWER The result is 3600 grams with two significant figures. the trailing or following zeros are not significant figures.  The answer in exponential notation is 3.6 x 103 grams. Here the zeros are not needed and all the digits are significant. .   2. How many significant figures are in the result for each of the following computations? ANSWER The result for 723.9 x 2.30  will have three significant figures because 2.30 has three sf The result for 0035.8 x 1.1 / 0.00024   will have two significant figures because 0.00024 has two sf The result for 123.67 x 0.007 will have 1 significant figure because the .007 quantity has only one sf.     3. How many significant figures are in the result for the sum of  720.34,          645.1,        245.897,         9984.   ANSWER The result for is 11595  with five significant figures.   4. How many significant figures are in the average for the series  124.57 mm,       124.72 mm,         124.56 mm ANSWER The average has four significant figures. the average is 124.6 mm because the first three digits are the same for all the measurements but the fourth digit differs so it is uncertain.   5. Give an example of an exact number.   ANSWER Exact numbers have an infinite number of significant figures. They are either counts or definitions. An example of a count would be the number of passengers in a car. Examples of definitions are i time dimension equalities  like 1 week = 7 days, 60 seconds = 1 minute unit definitions like  1 dozen = 12,      1 foot  = 12 inches,    1 yard  = 3 feet,   currency definitions like  1 dollar = 100 pennies