Physics Tutorial: Significant Figures
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Significant figures are the number of reliably known digits
used to locate a decimal point reported in a measurement. Proper
use of significant figures ensures that you correctly represent the
uncertainty of your measurements. For example, scientists
immediately realize that a reported measurement of 1.2345 m is much
more accurate than a reported length of 1.2 m.
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Care must be taken when determining the number of significant
figures to use. Your driver's license may state that your height
is 5 feet 3 inches, or 5.25 feet. Measuring a little more
carefully, we may find that your height is found to be 5.257 feet.
However if you said you were 5.257186 feet tall the scientific
community would look upon that measurement with serious skepticism
because you stated your height accurate to the nearest micron!
When a measurement is properly stated in scientific notation all
of the digits will be significant. For example: 0.0035 has 2
significant figures which can be easily seen when written in
scientific notation as 3.5 x 10-3. Fortunately, there are a few
general guidelines that are used to determine significant figures:
Whole Numbers: The following numbers are all represented by
three significant digits. Note that zeros are often
place holders and are not significant.
The following numbers are all represented by one significant
- 12300 (The zeros here often cause confusion. As written here,
the zeros are not significant. If they were, in fact,
significant, then the use of scientific notation would remove
all ambiguity and the number would be written 1.2300 x 104.)
The following numbers are all represented by four
Integers and Defined Quantities: Integers are assumed to
have an infinite number of significant figures. For example,
the 2 in C = 2pr, is exactly two and we can assume that the
number has an infinite number of significant figures. However,
the conversion factor 2.54 cm which is used to convert inches
to centimeters has three significant figures.
Multiplication and Division: When multiplying or dividing
numbers, the result should have only as many significant
figures as the quantity with the smallest number of
significant figures being used in the calculation. For
example, with your calculator multiply 4.7 and 5.93. The
calculator returns 27.871 as the answer. A common mistake
students make is to record what comes out of the calculator
as the correct answer. However, since 4.7 has only 2
significant figures, the result must be truncated to 2
significant figures as well. Taking all this into account
and remembering to round appropriately, the result should be
reported as 28.
Addition and Subtraction: When adding or subtracting
numbers, keep all figures up to the smallest quantity being
used in the calculation. For example, 3.14 + 0.00159 = 3.14159.
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