KD McMahon
Reseda Science Magnet
Unit 2: Measurement and Problem Solving in Chemistry
Summary:
Chemistry is a quantitative science. Chemists make many measurements and perform
numerous calculations in the process of their analyses. The student of chemistry must
become confident in his/her ability to make measurements and perform calculations in
chemistry.
Objectives:
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Discuss scientific notation
Explain metric units and prefixes and perform metric conversions.
Discuss uncertainty in measurement and significant figures.
Perform calculations using dimensional analysis.
I. Scientific Notation
Scientific notation is used to express and manipulate very large and very small
numbers conveniently. Scientific notation expresses a number between 1 and 10 and the
appropriate power of 10. The power of 10 depends on the number of places the decimal
point is moved and in which direction. The direction of the move determines whether the
power of 10 is positive or negative.
Example #1: Dinosaurs lived about 190,000,000 or 1.9 x108 years ago.
Example #2: Data can be accessed by a computer in 0.00000065 or 6.5 X 10-7 seconds.
Question #1: Perform the following conversions:
a.) 157,546,201  scientific notation
b.) .0157  scientific notation
c.) 7.58 X 104  standard notation
d.) 6.97 X 10-5  standard notation
II. International System of Units (SI)
Chemists use the International
System of Units (SI) or the metric
system for all chemical measurement.
The fundamental SI units include 
The SI system uses prefixes to alter the value of the units by multiples of 10.
When performing calculations using the metric system it is essential that all of the
prefixes are the same. To convert prefixes the number line below can be used.
Question #2: Perform the following conversions:
a.) 8.43 cm  mm
b.) 2.41 X 102 cm  mc
c.) 294.5 cL  hL
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d.) 1.445 X 10 m  km
e.) 2.54 X 10 Dg  mg
f.) 450.89 mL  L
III. Uncertainty in Measurement
A measurement always has some
degree of uncertainty. The uncertainty
of a measurement depends on the
measuring device and the measurer.
Precision and accuracy describe
uncertainty. Precision refers to the
degree of agreement among several
measurements of the same quantity.
Accuracy refers to the agreement of a
particular value with the true value.
A measurement includes "certain"
numbers and usually one "uncertain"
number.
All the certain numbers and the one
uncertain number in a measurement are
called "significant figures."
The number of significant figures for
a given measurement is determined
by the inherent uncertainty of the
measuring device.
The uncertainty in the last number is
assumed to be ± 1 unless otherwise
indicated.
Using Significant Figures
Rules for counting significant figures.
1. Nonzero integers always count as
significant figures.
2. There are three classes of zeros:
• Leading zeros never count,
• Captive zeros always count,
• Trailing zeros are significant only if the number contains a decimal.
Examples:
0.0108g ---> 3 sign figures
0.0050060g ---> 5 sign figures
5.030 X 103 ---> 4 sign figures
3. Numbers not obtained by measuring are called exact numbers. Exact numbers do not
limit the number of significant figures in calculations. Numbers not obtained by
measuring are called exact numbers. Exact numbers do not limit the number of
significant figures in calculations. Conversion factors are considered exact numbers.
Determining significant figures in calculations.
Multiplication & Division:
The number of significant figures in the result is the same as that in the measurement
with the smallest number of significant figures.
4.56 X 1.4 = 6.384 ---> 6.4
8.315 ÷ 298 = 27.902685 ---> 27.9
Addition & Subtraction:
The number of significant figures in the result is the same as the number with the smallest
number of decimal places.
12.11 +18.0 + 1.013 = 31.123 ---> 31.1
0.6875 - 0.1 = 0.5875 ---> 0.6
Question #3: Which of the following are exact numbers?
a.) The elevation of Breckenridge, Colorado is 9600 ft.
b.) There are 12 eggs in a dozen
c.) One yard is equal to 0.9144 m
Question #4: How many significant figures are in the following?
a.) 12 b.) 1098
c.)2001
d.) 100
e.) 0.0000101
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f.) 22.04030 g.) 2.001 X 10
h.) 4.800 X 10
Question #5: Round off each of the following numbers to three significant figures, and
write the answer in scientific notation.
a.) 312.54
b.) .00031254
c.) 31,254,000
d.) 0.31254
Question #6: Use scientific notation to express the number 480 to
a.) one significant figure
c.) two significant figure
b.) three significant figure
d.) four significant figure
Question #7: Perform the following mathematical operations, and express each result to
the correct number of significant figures.
a.) 97.381 + 4.2502 + 0.99195
b.) 171.5 + 72.915 – 8.23
c.) 0.102 X 0.0821 X 273
1.01
d.) 6.6262 X 10-34 X 2.998 X 108
2.54 X 10-4
e.) 14.78 cm X 1 inch (note: this is a conversion calculation)
2.54 cm
IV. Evaluating Measurements
In order to evaluate the accuracy of a measurement, you must be able to compare it to the
true or accepted value. The accepted value is a value based on reliable references.
The experimental value is the measured value determined in the experiment in the
laboratory.
The difference between the accepted value and the experimental value is the error. The
percent error is the error divided by the accepted value, expressed as a percentage of the
accepted value.
% error = ____error___
accepted value
x 100
Example: The melting point of silver chloride was measured to be 447 º C. The accepted
value is 455 ºC. What is the percent error in this measurement?
% error =
| 447ºC-455ºC| X 100%
455ºC
= 4.8351648% ---> 4.84%
Question #8: A student determined that the boiling point of an unknown solvent was
78.5°C. The actual value for this boiling point is 76.9°C. Calculate the percent error.
Question #9: A student determined that the density of an unknown metal to be
12.35 g/cm3. The lab instructor told the student that he had a percent error of 7.25%.
What was the actual density of the unknown metal?
V. Dimensional Analysis
Dimensional analysis is a systematic problem solving process by which one unit is
changed to another via conversion factors.
Steps in dimensional analysis:
To convert from one unit to another use the conversion factor that relates the two units.
Arrange the conversion factor ratio such that the unwanted units will cancel.
Multiply the quantity to be converted by the conversion factor to give the quantity with
the desired results.
Make sure you have the correct number of significant figures (remember, conversion
factors are exact numbers and do not limit the number of significant figures.
Check whether your answer makes sense.
Example: How many inches are in 62m?
62m X 100cm X 1 in = 2440.95in = 2400 in
1m
2.54cm
Question #10: