The following lesson is

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• The following lesson is
• one lecture in a series of
• Chemistry Programs
• developed by

Professor Larry Byrd Department of
Chemistry Western Kentucky University
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PART 2
Significant Figures
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II. Significant Figures
Every time a measurement of some physical
quantity is made, such as the mass of an object
or the volume of a solution, there is some
degree of uncertainty in the measurement.
This uncertainty is due to various factors,
such as, the accuracy of the device and the
skill of the person doing the measuring. The
recorded value for a measurement should give an
indication to the reader of its reliability.
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II. Significant Figures
Scientists have adopted a method of reporting
the reliability of measurements by using
what is known as significant figures. In
this procedure all numbers that are known with
certainty are recorded, plus a last number that
has been estimated (some uncertainty). All the
numbers in such recorded measurements are called
SIGNIFICANT FIGURES.
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The figure shows how the same volume of liquid,
when measured in Burets of different degrees of
possible accuracy will result in different
numbers of significant figures.
A
B
C
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The first buret is a 50 mL graduated buret that
has calibration marks every 10 mL.
A
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Buret B is a 50 mL graduated buret similar to A,
but it also contains marks every 1 mL.
A
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The Buret C has the best possibility of giving
the most accurate readings since it is a 50 mL
graduated buret that has calibration marks every
0.1 mL.
A
B
C
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Let us first look at the volume of the liquid in
Buret A. The liquid level is between the 30 mL
and 40 mL calibrated marks. Since the level
appears to be halfway between these two values,
we then record the measurement as 35 mL.
A
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However, the volume could be as small as 34 mL or
as large as 36 mL. The uncertainty in the
first measurement is one milliliter above () or
below (-) our estimated value or we can say that
the measurement is uncertain by /- 1 mL. The
recorded value of 35 mL, thus has two
significant figures (the number of certain
numbers plus one estimated!) the "3" is certain,
but the "5" is an estimate.
A
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In Buret B, the same volume of liquid is found
to be between 35 mL and 36 mL. However, if we
look very closely we can see that the level
appears to be slightly less than halfway between
these two values.
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By using this graduated buret we can be certain
that the volume is between 35 mL and 36 mL and we
can also estimate its value to the nearest
one-tenth of a milliliter (/- 0.1 mL). We
would report that the measured volume is 35.4 mL.
However, we must realize that this measurement
is uncertain by /- 0.1 mL, and the volume could
be as low as 35.3 mL or as high as 35.5 mL. The
reported value of 35.4 mL has three significant
figures since the "3" and "5" are certain and the
"4" is an estimate.
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When we observe the same volume in the last 50
mL graduated buret, we are now able to estimate
to the nearest /- 0.01 mL. We see that the
liquid's level is between the 35.4 mL and 35.5 mL
marks. Also, we can see that the level is
approximately halfway between the 35.4 mL and
35.5 mL marks. Thus, the volume is recorded to
be 35.45 mL. The measurement 35.45 mL is said to
have four significant figures.
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In summary, if we look at any reported
measurement, the uncertainty is assumed to be
/- one unit in the last recorded number.
For example, if a report has a mass of an
object as 11.6 grams, then it has three
significant figures and the measurement has an
uncertainty of /- 0.1 of a gram. If
11.62 grams is reported for an object, then the
measurement has four significant figures and the
uncertainty of the measurement is /- 0.01
of a gram.
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Some other examples are as follows
Measurement The numbers that are certain The numbers that are uncertain Number of significant figures
(1) 36 mL "3" "6" 2
(2) 36.8 mL "3" and "6" "8" 3
(3) 4536 meters "4", "5", and "3" "6" 4
(4) 0.052 gram "5" "2" 2
(5) 95.00 cm "9", "5", and "0" "0" 4
cm "4" "3" 2
(6)