The Basics of Significant Figures
(C) - Copyright, 1996 F.W. Boyle, Jr.
Significant figures is sometimes referred to as significant
digits. The idea behind significant figures is that any
measurement has an associated significance and an associated
error. When the results of measurements are combined to produce
a new number (numerical value), the results can only be as good
as the poorer (least significant) measurement. The quality of
the value (known as accuracy) cannot improve simply by
multiplying a less accurate value by another more accurate
value. In other words, the poorness continues through.
Some examples of this are:
1) An estimate of the number of jelly beans in a jar is 3250.
An average jelly bean weight is found to be 1.2977 g. How much
do the jelly beans weigh?
In order to understand significant figures, we must look at each
First the number 3250 really only has 3 digits in it. The
trailing zero (0) is called a place holder and is not accurate
UNLESS the number is stated to be 3250.0. In this latter
form the number is said to be exact. For this problem the number
was not exact but was estimated to be 3250. In scientific
notation, 3250 is written as 3.25x103. Thus when
written in scientific notation it is easier to determine the
number of actual digits in a number.
The second number, 1.2977, has 5 digits and is already in
Since 3.25x103 has only 3 digits the maximum number of
digits acceptable for calculating the weight of all the jelly
beans is 3 digits.
To do the math we use ALL the digits thus:
3.25 X 103
4.21752 x 103
But our answer can only have 3 significant figures since the
least number of significant figures in the numbers being
multiplied is 3. So the next step is to look at the digit just
to the right of the last significant figure. In this case the
last significant figure is 1 and the number to the right of it is
7. So the number one will be rounded up to 2 and all the other
digits will be dropped. The answer is then:
4.22 x 103 g
There is no set number for significant figures. Each problem
must be judged on its own. It is really simple to determine the
least number of significant figures by counted how many
significant figures there are in each of the numbers being put
into the calculation. The one with the fewest digits sets the
maximum number of digits that can be kept in the final answer.
Now for some practice in counting significant figures.
This number appears to have 7 significant figures. However, the
leading zeros are simply placeholders. This means the zeros are
there only to keep the number values in their proper position.
The actual count of significant figures is 3, for the 3, 7, &
Again as written one might think this number had 8 significant
figures but like the zeros in the first example, trailing zeros
are placeholders and are not counted in the number of significant
figures. The actual number of significant figures in this number
is 4. Included in the count are the 6, the zero between the 6
and the 2, the 2 and the 7.
Try these numbers on your own:
6) 3.2 x 105