3.1
Ch. 3.1 – Measurements and Their
Uncertainty
How do measurements relate to
science?
3.1
A measurement is a quantity that has both a
number and a unit.
Measurements are fundamental to the
experimental sciences.
Scientific Notation
In Chemistry, we will use very LARGE
and very small numbers to measure and
count. E.g., 1 gram of hydrogen contains about
602,000,000,000,000,000,000 atoms of hydrogen –
this can be written 6.02 X 1023atoms of hydrogen; and
the mass of one atom of gold, 0.000 000 000 000 000
000 000 327g, can be written 3.27 X 10-22g.
3.1
Accuracy, Precision, and Error
It is important to be able to make
measurements and to decide whether
a measurement is correct.
How do you evaluate accuracy and
precision?
3.1
Just because a measuring device works, you
cannot assume it is accurate. The scale below
has not been properly zeroed, so the reading
obtained for the person’s weight is inaccurate.
3.1
Accuracy
• Accuracy is a measure of how close a
measurement comes to the actual or true
value of whatever is measured.
• To evaluate the accuracy of a measurement,
the measured value must be compared to
the correct value.
3.1
Determining Error
• The accepted value is the correct value
based on reliable references.
• The experimental value is the value
measured in the lab.
• The difference between the experimental
value and the accepted value is called the
error.
3.1
The percent error is the absolute value of the
error divided by the accepted value, multiplied
by 100%.
3.1
3.1
Precision
• Precision is a measure of how close a
series of measurements are to one
another.
• To evaluate the precision of a
measurement, you must compare the
values of two or more repeated
measurements.
3.1
Accuracy = amount by which a
measurement deviates from true value - how
well you've actually done in making the
measurement
Precision = how many decimal places
(significant figures) can you determine
through your measurement - how well you
think that you've done in making the
measurement
Consider a ruler marked in cm vs. one marked in
mm
you can get a more precise measurement from
the mm ruler
but, if the ruler is marked incorrectly (say, the
spacings between marks vary), your
measurement cannot be accurate
3.1
Significant Figures in Measurements
Why must measurements be
reported to the correct number of
significant figures?
3.1
The significant figures in a measurement
include all of the digits that are known, plus a
last digit that is estimated.
3.1
When is a digit in a measurement
significant?
 All nonzero digits (24.7m, 0.743m, 714m)
 All zeros between nonzero digits (7003m,
40.79m, 1.503m)
Placeholder zeros to the left of nonzero digits
(0.0071m, 0.42m, 0.000099m) *Write using scientific
notation
 Trailing zeros with a decimal point
(43.00m,1.010m, 9.000m)
Trailing zeros without a decimal point are just
placeholders (300m, 7000m, 27,210m) *Write using
scientific notation if zeros are significant
There are two cases in which the
significant figures are unlimited and
therefore do not limit the precision of your
calculations.
o Counting in which you have an exact number
(27 people in the room)
o Defined quantities (60 min=1 hour, 100 cm = 1m)
for Conceptual Problem 3.1
3.1
Significant Figures in Calculations
How does the precision of a
calculated answer compare to the
precision of the measurements used
to obtain it?
3.1
In general, a calculated answer cannot
be more precise than the least precise
measurement from which it was
calculated.
3.1
Rounding
The calculated value must be rounded to make
it consistent with the precision of the
measurements from which it was calculated.
First decide how many sig figs your answer
should have. The answer depends on the
given measurements and on the mathematical
process used to arrive at the answer.
3.1
for Sample Problem 3.1
3.1
Addition and Subtraction
The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as the
measurement with the least number of decimal
places.
3.2
3.2
for Sample Problem 3.2
3.1
Multiplication and Division
• In calculations involving multiplication and
division, you need to round the answer to the
same number of significant figures as the
measurement with the least number of
significant figures.
• The position of the decimal point has nothing
to do with the rounding process when
multiplying and dividing measurements.
3.3
3.3
for Sample Problem 3.3
3.1 Section Quiz
1. In which of the following expressions is the
number on the left NOT equal to the number
on the right?
a. 0.00456  10–8 = 4.56  10–11
b. 454  10–8 = 4.54  10–6
c. 842.6  104 = 8.426  106
d. 0.00452  106 = 4.52  109
3.1 Section Quiz
2. Which set of measurements of a 2.00-g
standard is the most precise?
a. 2.00 g, 2.01 g, 1.98 g
b. 2.10 g, 2.00 g, 2.20 g
c. 2.02 g, 2.03 g, 2.04 g
d. 1.50 g, 2.00 g, 2.50 g
3.1 Section Quiz
3. A student reports the volume of a liquid as
0.0130 L. How many significant figures are in
this measurement?
a. 2
b. 3
c. 4
d. 5
END OF SHOW