Mathematical Operations with
Significant Figures
• When completing math calculations, the
final answer must be reported rounded to
the appropriate number of significant
figures.
• The answer is rounded according to the
LAST mathematical operation completed.
Rules
• 1. Complete calculations following the
order of operations.
• 2. If the FINAL step is MULTIPLICATION
or DIVISION:
– A. Look at each value given in the problem
and find the one with the LEAST number of
significant figures.
– B. Round the FINAL ANSWER to the same
number of significant figures.
– DO NOT ROUND UNTIL THE FINAL STEP!
Mult/Div Examples
•
4.59 X 1.22 = 5.5998
(3 sf) (3 sf)
=5.5998 =
=5.60 (3sf)
•
•
•
•
•
45.6
0.002454
(3 SF)
(4 SF)
= 18581.90709
= 18581.90709
= 18600
or convert to scientific notation and round = 1.86 x 104
•
ADD/SUBTRACT
• Complete calculations following order of
operations.
• If the FINAL step is addition or subtraction:
– A. Only consider SF to the RIGHT of the
decimal.
– B. Determine the FEWEST SF to the right of
the decimal.
– C. Round FINAL ANSWER to this number of
significant figures.
ADD/SUBTRACT EXAMPLES
25.4
63.66
+ 102.44
191.50
= 191.50
= 191.5
(1SF)
(2 SF)
(2 SF)
• 15.000 – 2.3791 = 12.6209
•
(3 sf)
• = 12.6209
(4 sf)
=
12.621