Significant Figures

In calculating problems related to science or when measuring something, it is important that everyone knows significant figures.  Significant figure is a number that contains certain digits and one uncertain digit. In measuring, we approximate the last digit that is why it is called uncertain digit, at the same time when calculating we round off the last digit that is why it is uncertain digit.

Guidelines in Identifying Significant Figures

In scientific work we must be always careful in writing the proper number of significant figures.  Below are the rules in identifying significant figures.

1.  Any digit that is not zero is a significant figure.  Let say for example 315 cm shows 3 significant figures, 4,367 has 4 significant figures.

2.  Zeros in between nonzero digits are significant.  Example 2002 m has 4 significant figures, 40, 505 g has 5 significant figures.  Zeros become significant because it is in between nonzero digits.

3.  Zeros to the left of the first nonzero digit are not significant.  They are only used to determine the placement of the decimal point.  For example, 0.007 g has only one significant figure and 0.00034 has two significant figures.

4. If a number is greater that 1, zeros to the right are significant if it contains decimal point.  Example, 1.0 m has two significant figures, 20.000 cm has five significant figures.  And if the number is less that 1 only zeros to the right are significant.  For example, 0.000240 g has 3 significant figures, 0.000300 m has also 3 significant figures.

5.  For a number that does not have decimal point, the trailing zeros to right may or may not be significant.  Thus if we have 300 cm, there can be 1, 2 or 3 significant figures.  Now to avoid ambiguity, we can write the number in scientific notation.  The number 300 can be written as 3 x 10², which has 1 significant figure only, it can also be 3.0 x 10², this time has 2 significant figures and 3.00 x 10², can have 3 significant figures.


Example: 
Determine the number of significant figures in the following measurements:
a.  5.02 g
b.  0.03459 cm
c.  478 kg
d.  85.0 L
e.  1.330 x 10²² atoms

Solution:
a. There are  3 significant figures because zeros in between nonzero digits are significant,
b. There are 4 significant figures, zeros to the left are not significant.
c.  There are 3 significant figures, all non zero digits are significant.
d. Also has 3 significant figures, zeros to the right are significant if there is decimal point.
e.  There are 4 significant figures, zero to the right is significant because the number contains decimal point.


For addition, subtraction, multiplication and division of significant figures and rounding off the answers to proper number of significant figures just click HERE.