Adding, Subtracting, Multiplying and Dividing Significant Figures

I observed in my classes that my students are always asking if how many decimal places are they going to round off the result of their calculations.  As a student they must know how to handle significant figures in doing calculations in addition, subtraction, multiplication and division.  You may have correct answer but the way to round off your answer to proper number of significant figures also matters.

There are rules to follow in using significant figures in calculations.
1.  In addition and subtraction, the calculated result must be rounded off to proper number of digits following the number which has least number of digits after the decimal point.   Let us have an example

                                                 90.335   cm   (3 digits after the decimal point)

                                           +      2.1       cm   (1 digit after the decimal point)
                                           ______________
                                                92.435   cm
                                     or        92.4  cm is the final answer.

The result is rounded off to one digit after the decimal point following the rule that in rounding off, answer in addition and subtraction, it should follow the number which has least number of digits after the decimal point.

Now in rounding off numbers we have to consider the number to be dropped so that we can decide if the preceding digit can be retained or should be increased by 1.  If the number to be dropped is 5 and above, the preceding digit should be increased by 1 but if the number to be dropped is less that 5 the preceding digit should be retained.  In the above example, since there should be 1 digit after the decimal point, the number to be dropped is 3 which is less than 5 and so we retain the value of the preceding digit which is 4.

2.  In multiplication and division, the calculated result should be rounded off to proper number of significant figures following the value or number which has least number of significant figures.  Let us have an example:

2.8  x  4.5039  =  12.61092    or 13

The above example was rounded off to 13 having only two significant figures following the least number of significant figures from the given,  two significant figures for 2.8 and 5 significant figures for 4.5039.  

6.85  ÷  112. 04 = 0.061138879 or 0.0611

The calculation above was rounded off to 3 significant figures following the number of significant figures of 6.85.

Try this!

Solve the problem below and round off to proper number of significant figures.

1.  11,254.1 g + 0.1983 g

2.  66.59 L -  3.113 L

3.  8.16 m x  5.1355 

4.  0.0154 kg ÷ 88.3 mL

Solution:

 1.   11,254.1 g

     +         0.1983  g

     __________

       11, 254.2983 g should be rounded off to 11,254.3 g

2.   66.59 L

      - 3.113 L

    _________

      63.477 L and should be rounded off to 63.48 L

3.  8.16 m x 5.1355   =  41.90568 m  or 41.9 m

4.  0.0154 kg÷ 88.3 mL  =  0.00017444054 kg/mL   or  0.000174 kg/mL

You can also change your answer in number 4 to scientific notation 1.74 x 10^-4 kg/mL.