Significant Figures
What makes a number significant?
The word "significant" is defined as : 'representative of something'. Obviously, by the very
definition of the term, significant numbers are important. In science, the basic reason for
limiting our expression of a number to the significant figures is to indicate the precision of
measurement. This is done because a calculation using measurements cannot logically be more
accurate than the figures on which the measurements are made.
Rules:
1. All non-zero digits are significant. 3971874351298 (13 sig. fig.)
2. Zeros which start a number are never significant. 0.35 (2 sig. fig) .0000587 (3 sig. fig)
3. Zeros which are between other significant figures are significant. 2348762074003 (13
sf).
4. Zeros at the end of a number may be significant, if:
a. a decimal has been purposefully placed at the end of the number. 5000. (4 sig. fig)
38000 (2 sig. fig.)
b. they follow other known significant figures and the number starts with a decimal.
.0057200 (5 sig. fig.)
(When writing a number with a specified number of significant figures, we must again keep
the above rules in mind and sometimes it is necessary to round off and re-write a number
in exponential notation just so it will show the needed number of significant figures)
Example # 1: Change 50093 to 3 significant figures. 50093 = 50100
Example #2: Change 54000 to 6 significant figures. 54000 = 54000.0
Example #3: Change 7000 to 3 significant figures 7000 = 7.00 X 104
Rules for Calculations:
Remember when your math teacher always told you when to round off your answer and to
how many places past the decimal your answer should be expressed? Well, no more! In
science you always have a reason for rounding off a number and expressing it to a definite
number of total significant figures. It has to do with precision and accuracy involved with
original measurements. Thus, the student (and scientist) must decide how a final
calculation is to be expressed so that it displays an accurate and VALID answer.
1. A final answer cannot be more accurate than the original numbers used in the
calculations.
2. In multiplication and division the final answer cannot have more significant figures than
any of the numbers which are used in arriving at the answer, and in fact, the original
number which has the least number of significant digits is used as the basis for deciding
how many sig. fig. the final answer must have.
Example: 3.0 X 395.2 X 0.002 = 2.3712. However, the starting number with the least
number of significant figures is 0.002, which has only 1 sig. fig. Thus, the final answer
must be rounded off to 2.
3. In addition and subtraction the final answer must be rounded off so that it displays no
more places past the decimal than that original number which has the LEAST number of
places past the decimal.
Example: 54.67 + 54.32 +54.0 + 54.777 + 54 = 271.767 The final answer here is 272
4. In doing dimensional analysis or multistep problems, do not round off any numbers
until the final step has been completed.
5. In conversion problems, the actual conversion factor is not to be considered in the rules
for rounding off since the reason for expressing numbers to a certain number of significant
figures is based on accuracy of an observed measurement.