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By: S. Roberts 4/2/09
Significant Figures are the minimum amount of digits required to report a value without loss of
accuracy. “It is important to use significant figures when recording a measurement so that it does not
appear to be more accurate than the equipment is capable of determining.”(Fetterman, 2007) For
example, when using a ruler that only measures inches (it doesn’t have little marks for tenths of inches)
you can’t measure something accurately to the thousandth’s place because the ruler doesn’t go up that
high.
Significant Digits
Rule for Determining
Sig Figs
Nonzero digits are always significant
Digits to the left of a decimal point are always
significant
Zeroes between significant figures are significant
Placeholders (0’s that indicate position of a decimal
point) are NOT significant
Zeroes at the end of a decimal point are significant
Example
# of
Sig Figs
257
3
3.5
92.
360.
1,003
6.0001
210
0.003
0.320
0.0045000
2
2
3
4
5
2
1
3
5
(Louisiana iLEAP)
Problem
Solution
1.) How many significant figures are in the number
34.0900?
1.) Using the rules for determining sig figs, the answer to
the problem is 6. We know this because all nonzero digits
are sig figs, and 0’s between sig figs are significant, and
also numbers that come after the decimal after a sig fig are
significant as well, so all of the numbers in the problem are
significant.
2.) The answer to this problem is 2 because when you use
the rules for determining whether figures are significant or
not, only 2 follow the criteria. Because there are no sig figs
in front of the decimal point, all of the zeroes in front of the
three are NOT significant because they don’t have sig figs
on both sides of them. And as for the sig fig at the end, it is
significant because it comes after a sig fig.
2.) How many significant figures are in the number
0.0000000030?
3.) Round the measurement of the image to the correct
sig figs.
3.) The answer to the problem is about 6.7. When
measuring things using sig figs, you include the numbers
you know for sure along with one estimated digit. We
know for sure that the image is somewhere between 6 and 7
inches. Because there are no tick marks between the two
measures, we can guess ONE digit. Some people may see
6.7, others, 6.8 or even 6.6. Sig figs are the number of
digits believed to be correct by the person doing the
measuring (2008). So, if you estimated more digits, your
reading would become less precise. You can’t just
randomly guess numbers, saying that the measure of the
image was 6.7485297635 because there’s no way to justify
those numbers without the tick marks.
4.) Round the measurement of the image to the nearest
sig figs.
4. Rounded to the nearest sig figs, the measurement of the
image is 6.73. Although it is the exact same image as the
one in problem #3, the ruler has more tick marks, and the
person doing the measuring can get a more precise reading.
Sig figs consist of all of the known digits and one estimated
digit. The 6 and the 7 are known because the ruler tells us.
But the 3 is unknown because the ruler doesn’t have a mark
for the hundredths place. The image could have well been
measured as 6.74 or 6.72 and would not have been wrong.
Adding/subtracting numbers
and determining Sig Figs
5.) First line up the decimals.
If you add these numbers together, you will get:
5.) You have 4.7832 grams of salt and 1.234 grams of
sugar and 2.02 grams of flour. If you combine these,
how many grams, in significant figures, will you get
total?
To make sure your answer has the correct amount of
significant figures, for adding/subtracting you go with the
least number of decimal places present. Here the last
number (2.02) has 2 decimal places; therefore, you round
your answer to 2 decimal places..
Multiplying/dividing numbers
and determining Sig Figs
6.) First you multiply regularly.
6.) Multiply 2.8723 by 1.6. Give your answer to the
correct number of sig figs.
When multiplying and dividing you round to the least
number of sig figs. Now count sig figs in each factor. The
first number has 5 sig figs. The second (1.6) has 2 sig figs.
Now round your answer in such a way that there will only be
2 sig figs. It helps to start at the left of your answer then
round. Sometimes it will be necessary to write your answer
in scientific notation to get the right amount of sig figs.
References
Fetterman, Lewis M. (2007). Significant Figures. Retrieved April 2, 2009, from
http://www.campbell.edu/faculty/fetterman/Significant%20Figures.htm
Significant figures. (2008). Math skills review: significant figures. Retrieved August 13, 2008, from
http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html
Louisiana iLEAP test preparation and intervention. Illinois: McDougal Littel.