Metric system
Measurements
Significant figures
Relationships
 Factor Label Method
SYSTEM OF MEASUREMENTS (SI)
SI Base Units
Derived SI Units
• Combinations of SI base units form derived units.
• pressure is measured in kg/m•s2, or pascals
Temperature can be measured using three different units
Conversion between T units
°F = 9/5 °C + 32
OR
°F = 1.8 °C + 32
K = °C + 273.15
T__G__M__KHD_dcm__μ__n__p__f
e
r
a
i
g
a
e
g
a
i e e
l c k
o t a
o
1 kg = 1000 g
1 kJ = 1x105 cJ
eei
cnl
i t l
i i
i
c
r
o
a
n
o
i
c
o
1 dm = 1x108 nm
1 cL = 10000 μL or 1x104 μL
e
m
t
o
Accuracy and Precision
Three students perform the same experiment:
The density of the metal is 4.2845 g/mL
Density values
(g/mL)
Joy
Taylor
Simon
Trial 1
2.4563
2.2846
4.2867
Trial 2
1.6798
2.2798
4.2904
Trial 3
4.7893
2.2901
4.2896
Accuracy and Precision, continued
Percentage Error
• Percentage error is calculated by subtracting the
accepted value from the experimental value, dividing
the difference by the accepted value, and then
multiplying by 100.
Percentage error =
Valueexperimental -Valueaccepted
Valueaccepted
 100
• Sample Problem
• A student measures the mass and volume of a
substance and calculates its density as 1.40 g/mL. The
correct, or accepted, value of the density is 1.30 g/mL.
What is the percentage error of the student’s
measurement?
Use of Numbers
• Exact numbers
– 1 dozen = 12 things for example
• Accuracy
– how closely measured values agree with
the correct value
• Precision
– how closely individual measurements
agree with each other
Use of Numbers
• Significant figures
– digits believed to be correct by the person
making the measurement
• Exact numbers have an infinite number
of significant figures
12.000000000000000 = 1 dozen
because it is an exact number!!!!
Use of Numbers
Significant Figures - Rules
• Leading zeroes are never significant
0.000357 has three significant figures
• Trailing zeroes only significant if after decimal
point.
2.7800 has five significant figures
• Use scientific notation to remove doubt
2.40 x 103 has 3 significant figures
2.400x103 has 4 significant figures
2400 has only two significant figures.
Use of Numbers
• Imbedded zeroes are always
significant
3.0604 has five significant figures
Use of Numbers
• Multiplication & Division rule
Easier of the two rules
Product has the smallest number of
significant figures of multipliers
2.7832
4.242
x 1.23
x 1.4
5.21766
round off to 5.22
3.89648
round off to 3.9
Sample Problem.
Calculate the density of a substance with a
mass of 14.78 g and a volume of 10.3 mL
Use of Numbers
• Addition & Subtraction rule
More subtle than the multiplication rule
Answer contains smallest decimal place of the
addends.
3.6923
 1.234
 2.02
6.9463
round off to 6.95
8.7937
 2.123
6.6707
round off to 6.671
Sample problem
Determine the perimeter of a piece of paper of
27.94 cm long and 6.92 cm wide.
• Sample Problem
• How many significant figures are in each of
the following measurements?
•
•
•
•
•
a. 28.6 g
b. 34.40 cm
c. 910 m
d. 0.046 04 L
e. 0.006 700 0 kg
Chapter 2
Direct Proportion
•Two quantities are directly
proportional to each other
if dividing one by the other
gives a constant value.
Chapter 2
Direct Proportion
Inverse Proportion
Two quantities are
inversely proportional to
each other if multiplying
one by the other gives a
constant value.
Chapter 2
Inverse Proportion
The Unit Factor Method
• Simple but important method to get correct
answers in word problems.
• Method to change from one set of units to
another.
The Unit Factor Method
• fractions represent unit factors
1 ft
1 ft = 12 in becomes
12 in
or
12 in
1 ft
The Unit Factor Method
• Example: Express 9.32 meters in micrometers.
The Unit Factor Method
• Example: Express 627 milliliters in L.
The Unit Factor Method
• Example: Express 45.8 kg in mg.
Density conversions
• Example: A 20.0 g irregular solid is introduced
in a graduated cylinder. The level of water
inside the graduated cylinder when from 20.0
mL to 23.3 mL. Calculate the density of the
solid.
Density conversions
• Example: What volume will occupy a liquid
with a mass of 15.7 g and a density of
1.34g/mL?
Density conversions
• Example: Calculate the mass of a gas that
occupies 1.5 L and it has a density of
0.00143g/mL?