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Significant Figures
In chemistry it is often impossible to obtain
the exact value of the quantity under
investigation. For this reason, it is important
Significant
Figures
to indicate the margin
of error in a
measurement by indicating the number of
significant figures.
Significant figures are the meaningful digits
in a measured or calculated quantity up to
and including the first uncertain digit.
A graduated cylinder reads 6.0 mL. 6.0 mL
implies 6.0 ± 0.1 mL so the actual volume is
somewhere between 5.9 mL and 6.1 mL.
The number of significant figures in a
measurement ensures that calculations
involving the data will reflect the precision of
the measuring device.
In all cases the last digit is always
uncertain and amount of this
uncertainty depends on the particular
measuring device used.
Suppose that three people were told to
determine the length of a piece of tile and
were given a ruler whose smallest
markings were at 0.1 cm intervals.
They report the following values:
Student 1
Student 2
Student 3
1.35
1.3
1.354
Who is right? Who has reported a value of
the proper accuracy?"
Rules for Significant Figures
Any digit that is not zero is significant, 725
m has 3 significant figures
Zeros between nonzero digits are
significant (captive zeros), 40,703 kg has 5
significant figures
Zeros to the left of the first nonzero digit
(leading zeros) are not significant.
0.000045 g contains 2 significant figures.
The zeros simply indicate the placement of
the decimal point
If a number does not contain a decimal
point and trailing zeros, the zero may or
may not be significant. 500 cm may have
1 (5), 2 (50), or 3 (500) significant figures.
More info is needed to know which one is
correct.
Adding and Subtracting
The number of sig figs to the right of the
decimal point in the final sum or difference
is determined by the smallest number of
decimal places in any of the original
numbers.
89.432 + 1.1 = 90.532 round to 90.5
2.097 - 0.12 = 1.977 round to 1.98
Multiplication and Division
The number of sig figs in the final product
or quotient is determined by the original
number that has the smallest number of
significant figures.
2.8 x 4.5039 = 12.61092 round to 13
6.85/112.04 = 0.0611388789 round to
0.0611
One more wrinkle…
Exact numbers obtained from definitions or by
counting numbers of objects have an infinite
number of significant figures.
Let’s assume a brick weighs 5.372 lbs. Then the
weight of 5 bricks is
5.372 lbs x 5 = 26.86
You do not round off this product to one sig fig.
because 5 is 5.00000…. by definition