The Box-and-Dot Method:
A Simple Strategy for Counting Significant Figures
There are a number of ways for determining the number of significant digits in a measurement. There are
convoluted sets of rules involving digits to the right and left of decimal points. And there have been
suggestions as simple as count all the digits and subtract the “place holding zeros”. The method
described below is one of the better ways. It comes from W. Kirk Stephenson, Division of Science and
Mathematics, Angelina College, Lufkin, TX 75901; kstephenson@angelina.edu
http://pubs.acs.org/doi/pdf/10.1021/ed086p933
Suppose we what to determine the number of significant digits in the following measurement. In this
method a “dot” is the decimal point.
0.001230400
Step 1 - Draw a box around all nonzero digits, beginning with the leftmost nonzero digit and ending with
the rightmost nonzero digit in the number, including any sandwiched zeros.
0.001230400
Step 2 - If a dot is present, draw a box around any trailing zeros.
0.001230400
Step 3 - All the boxed digits are significant.
There are 7 significant digits
Examples:
34,034 has five significant digits
3400 has two significant digits
0.0034 has two significant digits
0.003400 has four significant digits
Determine the number of significant digits in each of the following measurements.
1.
35.0 cm
6.
3.000 L
2.
0.00050 kg
7.
0.03040 m
3.
4530 km
8.
240 mL
4.
30.02 m
9.
3.40 x 106 Hz
5.
13,500 years
10. 8.3010 x 10-3 m