Chapter 3: Measurement
CMH 101 Luca Preziati
Measurement DEF
= Quantitative observation
• Comparison to an agreed upon standard
• Every measurement has a number and a unit
Scientists have measured the average
global temperature rise over the past
century to be
The number tells you
1.what multiple of the
standard the object
measures
2.the uncertainty in the
measurement
0.6 °C
The unit
tells you what standard you
are comparing your object to
Chapter 3: Measurement
Scientific Notation is a way of writing large and small numbers
The sun’s diameter is
1,392,000,000 m
The sun’s diameter is
1.392 x 109 m
An atom’s average diameter is
0.000 000 000 3 m
An atom’s average diameter is
3 x 10-10 m
Large Number = Positive Exponent
Small Number = Negative Exponent
1.392 x 109 m
3 x 10-10 m
Chapter 3: Measurement
Writing a number in scientific notation
1,392,000,000 m
1. Locate the decimal point
2. Move the decimal point until a number
between 1 and 10 is obtained
3. Multiply the new number by 10n
4. n is the number of places you moved
the decimal point
5. Large number? n is positive
Small number? n is negative
.
1,392,000,000 m
1.392,000,000. m
1.392 x 10 ? 9 m
1.392 x 10 9 m
3.5 : Significant Figures (Pg. 69)
Significant Figures Writing Numbers to Reflect Uncertainty
Exact Values
• Can be obtained by counting or by definition
• Exact values have “unlimited (∞) significant figures”
Measurements
• Are obtained from instruments
• The number of significant figures reflects the
instrument Uncertainty. All the digits written are
known with certainty except the last one, which is an
estimate
1.2 grams
Certain
Estimated (Doubtful)
3.5 : Significant Figures (Pg. 69)
Counting Significant Figures
1. Write the number in scientific notation
2. Count the number of figures
0.000 000 000 35 m
3.5 x 10-10 m
2 Significant figures
Note: Zeros at the end of a number without a written decimal point are
ambiguous and should be avoided by using scientific notation.
if 150 has 2 sig. figs. then 1.5 x 102
but if 150 has 3 sig. figs. then 1.50 x 102
3.5 : Significant Figures (Pg. 69)
Counting Significant Figures
1: Non zero digits are always significant.
Thus 6.23 km has three significant figures.
2: Zeros in the middle of a figure are always significant.
Thus 56.0309 g has 6 significant figures.
3: Zeros at the beginning of a number are only decimal place holders; they are
not significant.
Thus 0.00928 cm has three significant figures.
4: Zeros at the end of a number but after the decimal point are significant.
Thus 21.30 mL has four significant figures.
5: Zeros at the end of a number but before the decimal point are ambiguous.
Thus 21,000 kg has 2 significant figures, but 21,000.0 has 6 significant figures
(rule 4).
3.5 : Significant Figures (Pg. 69)
Counting Significant Figures. Examples.
How many significant figures are in each of the following numbers?
0.0035
1.080
2371
2.97 × 105
1 dozen = 12
100,000
3.5 : Significant Figures (Pg. 69)
+-
Addition and Subtraction with Significant Figures
When adding or subtracting measurements with significant figures, the result has
the same number of decimal places as the measurement with the fewest number of
decimal places
5.74 +
2 dec. pl.
4.8 1 dec. pl
0.823 +
3 dec. pl.
3.965
3 dec. pl.
2.651 = 9.214 = 9.21
3 dec. pl.
=
0.835 =
2 dec. pl.
0.8
1 dec. pl.
3.5 : Significant Figures (Pg. 69)
× ÷
Multiplication and Division with Significant Figures
When multiplying or dividing measurements with significant figures, the result has
the same number of significant figures as the measurement with the fewest number
of significant figures
5.02 ×
3 sig. figs.
89,665 ×
5 sig. figs.
5.892 ÷
4 sig. figs.
0.10 = 45.0118 = 45
2 sig. figs.
2 sig. figs.
6.10 = 0.96590 = 0.966
3 sig. figs.
3 sig. figs.
3.4 : Units (Pg. 63)
The Standard Units
Scientists have agreed on a set of international standard units for comparing all
our measurements called the SI units
Système International = International System
Quantity
Unit
Symbol
length
meter
m
mass
kilogram
kg
time
second
s
kelvin
K
temperature
3.4 : Units (Pg. 63)
Related Units in the SI System
• All units in the SI system are related to the standard unit by a power of 10
• The power of 10 is indicated by a prefix
• The prefixes are always the same, regardless of the standard unit
3.4 : Units (Pg. 63)
Common Prefixes in the SI System (pg.65)
Prefix
Symbol
Decimal
Equivalent
Power of 10
1,000,000
Base x 106
1,000
Base x 103
mega-
M
kilo-
k
deci-
d
0.1
Base x 10-1
centi-
c
0.01
Base x 10-2
milli-
m
0.001
Base x 10-3
micro-
m or mc
0.000 001
Base x 10-6
nano-
n
0.000 000 001
Base x 10-9
3.4 : Units (Pg. 63)
Mass
• = Measure of the amount of matter present in an
object
• SI unit = kilogram (kg)
 about 2 lbs. 3 oz.
• Commonly measure mass in grams (g) or
milligrams (mg)
 1 kg = 2.2046 pounds, 1 lbs. = 453.59 g
 1 kg = 1000 g = 103 g,
 1 g = 1000 mg = 103 mg
 1 g = 0.001 kg = 10-3 kg,
 1 mg = 0.001 g = 10-3 g
DEF
3.4 : Units (Pg. 63)
Length
• = Measure of the two-dimensional distance an object covers
• SI unit = meter
 About 3½ inches longer than a yard
• 1 meter = one ten-millionth the distance from the North Pole to
the Equator = distance between marks on standard metal rod in
a Paris vault = distance covered by a certain number of
wavelengths of a special color of light
• Commonly use centimeters (cm)
 1 m = 100 cm
 1 cm = 0.01 m = 10 mm
 1 inch = 2.54 cm (exactly)
DEF
3.4 : Units (Pg. 63)
Volume
• = Measure of the amount of three-dimensional space occupied
• SI unit = cubic meter (m3)
 a Derived Unit
• Commonly measure solid volume in cubic centimeters (cm3)
 1 m3 = 106 cm3
 1 cm3 = 10-6 m3 = 0.000001 m3
• Commonly measure liquid or gas volume in milliliters (mL)
 1 L is slightly larger than 1 quart
 1 L = 1 dL3 = 1000 mL = 103 mL
 1 mL = 0.001 L = 10-3 L
 1 mL = 1 cm3
DEF
3.6 : Metric-USCS Conversions (Pg. 77)
Common Units and Their Equivalents
Length
1 kilometer (km)
=
0.6214 mile (mi)
1 meter (m)
=
39.37 inches (in.)
1 meter (m)
=
1.094 yards (yd)
1 foot (ft)
=
30.48 centimeters (cm)
1 inch (in.)
=
2.54 centimeters (cm) exactly
1 kilogram (kg)
=
2.205 pounds (lb)
1 pound (lb)
=
453.59 grams (g)
1 ounce (oz)
=
28.35 (g)
Mass
3.6 : Metric-USCS Conversions (Pg. 77)
Common Units and Their Equivalents
Volume
1 liter (L)
=
1000 milliliters (mL)
1 liter (L)
=
1000 cubic centimeters (cm3)
1 liter (L)
=
1.057 quarts (qt)
1 U.S. gallon (gal)
=
3.785 liters (L)
3.3 : Dimensional Analysis (Pg. 56)
Problem Solving and Dimensional Analysis
• Arrange conversion factors so starting unit cancels
 Arrange conversion factor so starting unit is on the bottom
of the conversion factor
• May string conversion factors
 So we do not need to know every relationship, as long as
we can find something else the beginning and ending
units are related to
unit 1 = unit 2
unit 1
x
unit 2
unit 1
=
unit 2
3.3 : Dimensional Analysis (Pg. 56)
Dimensional Analysis Example 1: Convert 7.8 km to miles
1.
Write down the Given
quantity and its unit
Given:
7.8 km
(unit 1)
2.
Write down the quantity you
want to Find and unit
Wanted:
? Miles
(unit 2)
3.
Write down the appropriate
Conversion Factors
Conversion
Factors:
4.
Rearrange the conversion
Factor
Solution:
1 km = 0.6214 mi
7.8 km 
0.6214 mi
 4.84692 mi
1 km
5.
Sig. Figs. and Round
Round:
4.84692 mi = 4.8 mi
6.
Check
Check:
Units & Magnitude are
correct
3.3 : Dimensional Analysis (Pg. 56)
Dimensional Analysis Example 2: Convert 20.0 lbs to kg
1.
Write down the Given
quantity and its unit
Given:
20.0 lbs
(unit 1)
2.
Write down the quantity you
want to Find and unit
Wanted:
? kg
(unit 2)
3.
Write down the appropriate
Conversion Factors
Conversion
Factors:
4.
Rearrange the conversion
Factor
Solution:
1 kg = 2.205 lbs
20 lbs 
1 kg
 9.07029 kg
2.205 lbs
5.
Sig. Figs. and Round
Round:
9.07029 kg = 9.07 kg
6.
Check
Check:
Units & Magnitude are
correct
3.3 : Dimensional Analysis (Pg. 56)
Dimensional Analysis Example 3: How many milliliters in 1.00 qt?
1.
Write down the Given
quantity and its unit
Given:
1.00 qt
(unit 1)
2.
Write down the quantity you
want to Find and unit
Wanted:
? mL
(unit 2)
3.
Write down the appropriate
Conversion Factors
Conversio
n Factors:
5.
Rearrange the conversion
Factor
Solution:
1 L = 1.057 qt
1 L = 1000 mL
1.00qt x
__1 L__
= 0.94607 L
1.057 qt
0.94607L x 1000 mL = 946.07mL
1L
6.
Sig. Figs. and Round
Round:
946.07 mL = 946 mL
7.
Check
Check: Units/Magnitude correct
3.7 : Temperature (Pg. 81)
Temperature
•
•
DEF
= measure of the average kinetic energy of the molecules in a
sample
SI unit = Celsius (°C)
Water
Fahrenheit
Celsius
Kelvin
Freezing
point
32
0
273
Boiling
Point
212
100
373
C 
F - 32
1.8
K  C  273.15
3.8 : Density (Pg. 84)
Volume vs Mass of Brass
y = 8.38 x
160
140
120
Mass, g
100
80
60
40
20
0
0.0
2.0
4.0
6.0
8.0
10.0
Volume, cm3
12.0
14.0
16.0
18.0
3.8 : Density (Pg. 84)
Ratio of mass:volume
Density 
Mass
Volume
Solids = g/cm3
1 cm3 = 1 mL
Liquids = g/mL
Gases = g/L
Volume 
Mass
Density
Mass  Density  Volume
Volume of a solid can be determined by water displacement
Density : solids > liquids >>> gases
except ice is less dense than liquid water!
3.8 : Density (Pg. 84)
• For equal volumes, denser object has larger mass
• For equal masses, denser object has smaller
volume
• Heating objects causes objects to expand
 does not effect their mass!!
 How would heating an object effect its density?
• In a heterogeneous mixture, the denser object sinks
 Why do hot air balloons rise?
3.10 : Dimensional Analysis vs. Algebra (Pg. 88)
Density (and Temperature) use equations instead of conversion factors
• Example 1: the gasoline in an automobile gas tank has a mass of 60.0 kg
and a density of 0.752 g/cm3. What is the volume?
• Given:
mass = 60.0 kg
Density = 0.752 grams/cm3
• Wanted: Volume in L
• Conversion Factors:
1000 grams = 1 kg
• Example 2: A 55.9 kg person displaces 57.2 L of water when submerged
in a water tank. What is the density of the person in g/cm3