Rules for using significant figures:

1) Non-zero integers always count as significant figures

ex: the number 1997 has four significant figures


2) Leading zeros (zeros that precede all of the non-zero digits) never count as significant figures. Leading zeros only serve as place holders.

ex: the number 0.0001 has one significant figure


3) Captive zeros (zeros that fall between nonzero digits) always count as significant figures

ex: The number 0.507 has three significant figures


4) Trailing zeros (zeros at the right end of the number) are significant only if the number contains a decimal point.

ex: The number 100. contains three significant figures

ex: The number 100 contains one significant figure


5) Exact numbers (numbers determined by counting or by definition) have an unlimited number of significant figures.

ex: If you have 39 people in a classroom, the number 39 has unlimited significant figures, because the number was attained by counting.

ex: The statement 1 inch = 2.54 cm comes from the definition of an inch, so neither 1 inch or 2.54 cm limits the number of significant figures within a calculation (when used as a conversion).


6) For multiplication or division the number of significant figures in the answer is the same as that in the measurement with the smallest number of significant figures.

ex: 4.56 x 1.4 = 6.384 round to 6.4 (two significant figures)

 

7) For addition or subtraction the limiting term is the term with the smallest number of decimal places.

ex: 12.11 + 18.0 + 1.013 = 31.123
BUT: The answer is rounded off to 31.1 (one decimal place)


8) When performing a calculation, do not round off sequentially: round off at the end.

9) Extra hints: If you have made a more accurate measurement than your number reflects, express the number in scientific notation to include all significant digits:

ex: A map scale with 4,200 ft was measured with precision greater than ten miles

Solution: express the result as 4.20 x 103 ft