Chapter 2
Scientific Measurement
Chapter 2 Goals
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Calculate values from measurements using the
correct number of significant figures.
List common SI units of measurement and
common prefixes used in the SI system.
Distinguish mass, volume, density, and specific
gravity from one another.
Evaluate the accuracy of measurements using
appropriate methods.
Introduction
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Everyone uses measurements in some form
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Deciding how to dress based on the temperature;
measuring ingredients for a recipes; construction.
Measurement is also fundamental in the sciences
and for understanding scientific concepts
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It is important to be able to take good
measurements and to decide whether a measurement
is good or bad
Introduction
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In this class we will make measurements and
express their values using the International
System of Units or the SI system.
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All measurements have two parts: a number and a
unit.
2.1 The Importance of Measurement
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Qualitative versus Quantitative Measurements
Qualitative measurements give results in a
descriptive, nonnumeric form; can be influenced by
individual perception
 Example: This room feels cold.
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2.1 The Importance of Measurement
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Qualitative versus Quantitative Measurements
Quantitative measurements give results in definite
form usually, using numbers; these types of
measurements eliminate personal bias by using
measuring instruments.
 Example: Using a thermometer, I determined that
this room is 24°C (~75°F)
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Measurements can be no more reliable than
the measuring instrument.
2.1 Concept Practice
1. You measure 1 liter of water by filling an empty 2liter soda bottle half way. How can you improve the
accuracy of this measurement?
2. Classify each measurement as qualitative or
quantitative.
a. The basketball is brown
b. the diameter of the basketball is 31 centimeters
c. The air pressure in the basketball is 12 lbs/in2
d. The surface of the basketball has indented seams
2.2 Accuracy and Precision
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Good measurements in the lab are both correct
(accurate) and reproducible (precise)
accuracy – how close a single measurement comes
to the actual dimension or true value of whatever is
measured
 precision – how close several measurements are to
the same value
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Example: Figure 2.2, page 29 – Dart boards….
2.2 Accuracy and Precision
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All measurements made with instruments are
really approximations that depend on the quality
of the instruments (accuracy) and the skill of the
person doing the measurement (precision)
The precision of the instrument depends on the
how small the scale is on the device.
The finer the scale the more precise the instrument.
 2.2 Demo, page 28
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2.2 Concept Practice
3. Which of these synonyms or characteristics
apply to the concept of accuracy? Which apply
to the concept of precision?
a. multiple measurements
b. correct
c. repeatable
d. reproducible
e. single measurement
f. true value
2.2 Concept Practice
4. Under what circumstances could a series of
measurements of the same quantity be precise
but inaccurate?
2.3 Scientific Notation
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In chemistry, you will often encounter numbers
that are very large or very small
One atom of gold = 0.000000000000000000000327g
 One gram of H = 301,000,000,000,000,000,000,000 H
molecules
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Writing and using numbers this large or small is
calculations can be difficult
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It is easier to work with these numbers by writing them
in exponential or scientific notation
2.3 Scientific Notation
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scientific notation – a number is written as the
product of two numbers: a coefficient and a
power of ten
Example: 36,000 is written in scientific notation
as 3.6 x 104 or 3.6e4
Coefficient = 3.6 → a number greater than or equal
to 1 and less than 10.
 Power of ten / exponent = 4
 3.6 x 104 = 3.6 x 10 x 10 x 10 x 10 = 36,000
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2.3 Scientific Notation
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When writing numbers greater than ten in
scientific notation the exponent is positive
and equal to the number of places that the
exponent has been moved to the left.
2.3 Scientific Notation
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Numbers less than one have a negative
exponent when written in scientific notation.
Example: 0.0081 is written in scientific notation as
8.1 x 10-3
 8.1 x 10-3 = 8.1/(10 x 10 x 10) = 0.0081
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When writing a number less than one in
scientific notation, the value of the exponent
equals the number of places you move the
decimal to the right.
2.3 Scientific Notation
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To multiply numbers written in scientific notation,
multiply the coefficients and add the
exponents.
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(3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106
To divide numbers written in scientific notation,
divide the coefficients and subtract the
exponent in the denominator (bottom) from the
exponent in the numerator (top).
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(6 x 103)/(2 x 102) = (6/2) x 103-2 = 3 x 101
2.3 Scientific Notation
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Before numbers written in scientific notation are
added or subtracted, the exponents must be
made the same (as a part of aligning the
decimal points).
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(5.4 x 103)+(6 x 102) = (5.4 x 103)+(0.6 x 103)
= (5.4 + 0.60) x 103 = 6.0 x 103
2.3 Concept Practice
5. Write the two measurements given in the first
paragraph of this section in scientific notation.
a. mass of a gold atom =
0.000000000000000000000327g
b. molecules of hydrogen =
301,000,000,000,000,000,000,000 H molecules
2.3 Concept Practice
6. Write these measurements in scientific notation.
The abbreviation m stands for meter, a unit of
length.
a. The length of a football field, 91.4 m
b. The diameter of a carbon atom, 0.000000000154 m
c. The radius of the Earth, 6,378,000 m
d. The diameter of a human hair, 0.000008 m
e. The average distance between the centers of the
sun and the Earth, 149,600,000,000 m
2.1 Concept Practice
1. You measure 1 liter of water by filling an empty 2liter soda bottle half way. How can you improve the
accuracy of this measurement?
A: Use a more precise volumetric measure such as a
measuring cup.
2.1 Concept Practice
2. Classify each measurement as qualitative or
quantitative.
a. The basketball is brown - Qualitative
b. the diameter of the basketball is 31 centimeters
- Quantitative
c. The air pressure in the basketball is 12 lbs/in2
- Quantitative
d. The surface of the basketball has indented seams
- Qualitative
2.2 Concept Practice
3. Which of these synonyms or characteristics
apply to the concept of accuracy? Which apply
to the concept of precision?
a. multiple measurements - Precision
b. correct - Accuracy
c. repeatable - Precision
d. reproducible - Precision
e. single measurement - Accuracy
f. true value - Accuracy
2.2 Concept Practice
4. Under what circumstances could a series of
measurements of the same quantity be precise
but inaccurate?
A: when using an improperly calibrated measuring
device
2.3 Concept Practice
5. Write the two measurements given in the first
paragraph of this section in scientific notation.
a. mass of a gold atom =
0.000000000000000000000327g = 3.27 x 10-22g
b. molecules of hydrogen =
301,000,000,000,000,000,000,000 H molecules
= 3.01 x 1023 H molecules
2.3 Concept Practice
6. Write these measurements in scientific notation.
The abbreviation m stands for meter, a unit of
length.
a. The length of a football field, 91.4 m = 9.14 x 101 m
b. The diameter of a carbon atom, 0.000000000154 m = 1.54 x 10-10 m
c. The radius of the Earth, 6,378,000 m = 6.378 x 106 m
d. The diameter of a human hair, 0.000008 m = 8 x 10-6 m
e. The average distance between the centers of the sun and the
Earth, 149,600,000,000 m = 1.496 x 1011 m