Significant Figures

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* There is a difference between pure numbers (as used in math classes) and measured quantities (such as 35.6 mL of acid).

* Measurement tools often limit our ability to measure quantities.

* We must be aware of the accuracy limits of each piece of lab equipment that we use and record our data to the proper number of significant figures.

* You are always allowed one estimated figure in measurements.

* When measured quantities are given to you, it is assumed that the proper number of significant figures were recorded.  (all measurements in scientific notation must be recorded to the proper number of significant figures).

* When using conversions, `1' is considered to be correct to several significant figures.

Rules for Counting Significant Figures

Rule:  All non-zero digits are significant.
12.83 cm  [4]       16935 g  [5]

Rule:  Zeros between other significant figures are significant.
12 038 cm   [5]     169.04 g   [5]    70 304 g   [ ]      395.01 kg   [ ]

Rule:  Zeros to the right of a decimal point and to the right of a number are significant.
12.380 cm  [5]    169.00 m  [5]   3.010 mL  [4]    1.30 kg  [ ]   1691.100 cm  [ ]

Rule: A zero standing alone to the left of a decimal point is not significant.
0.421 g  [3]    0.5 m  [ ]

Rule:  Zeros to the right of the decimal and to the left of a number are not significant.
0.000 421 mg  [3]     0.001 80 cm  [3]     0.010 kg  [ ]     0.01010 m  [ ]

Rule: Zeros to the right of the last number but left of the decimal point may or may not be significant.  This information is known only to the person that made the measurement.  Use scientific notation when in doubt.  The use of a bar over the last significant zero is acceptable as well as using the decimal point to indicate that all digits to its left are significant.
4000. g   [4]    3400 kg   [2]     69 700. mL   [  ]     4.50 E 2 g   [ ]

Rounding Rules

When rounding examine the digit to the right of the digit that is to be last (this number is called the trigger):
a) if the trigger is less than 5, drop it and all the digits to the right of it
b) if the trigger  is more than 5, increase by 1 the number to be rounded
C) if the trigger is 5, round the number so that it will be even

Page Last Updated: Friday March 02, 2007           Webmaster: Larry Jones                 Pickens County School District