Pre - Calculus 10
TODAY:
• The Real Number System
• The Imperial vs. Metric System
Classifying Numbers
• In mathematics, numbers are classified according to
common characteristics.
• Every number is classified as belonging to one or more of
the following sets of numbers:
Natural Numbers:
N = { 1, 2, 3, …}
Whole Numbers:
W = { 0, 1, 2 , 3, ...}
Integers:
Rational Numbers:
I = {….. -3, -2, -1, 0, 1, 2, 3, ...}
a

Q   | a, b  I , b  0 

b

Irrational Numbers: Q = {non-terminating, non-repeating
decimals} π, e ,√2 , √ 3 ...
Classifying Numbers
• In mathematics, numbers are classified according to
common characteristics.
• Every number is classified as belonging to one or more of
the following sets of numbers:
Real Numbers:
R = {all rational and irrational}
𝟔 𝟖 𝟔𝟗𝟔
, , , π, e ,√2 , √ 3 ...
𝟓 𝟔
𝟕𝟓
Imaginary Numbers: i = {square roots of negative
numbers}
−𝟔𝟒,
−2
Complex Numbers: C = { real and imaginary numbers}
Complex Numbers
Real Numbers
Rational Numbers
Natural
Numbers
Imaginary Numbers
Whole Numbers
Irrational Numbers
Integers
1.1.3
Classifying Numbers
1.1.4
1.1 Imperial Measures of Length
Pages: 4 - 12
There are two types of measurements
we use
Pages: 10 - 20
The units on the following pictures are
the IMPERIAL units
Copyright © 2010 Ryan P. Murphy
What unit of measurement is this?
Copyright © 2010 Ryan P. Murphy
Gallon
What unit of measurement is this?
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Mph (Miles per hour)
Gallon
What unit of measurement is this?
Copyright
© 2010
Ryan
P. Murphy
Copyright
© 2010
Ryan
P. Murphy
Mph (Miles per hour)
Gallon
Pounds
What unit of measurement is this?
Copyright © 2010 Ryan P. Murphy
Mph (Miles per hour)
Gallon
Pounds
Inches
What unit of measurement is this?
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Mph (Miles per hour)
Gallon
Pounds
Inches
Yards
What unit of measurement is this?
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Mph (Miles per hour)
Gallon
Pounds
Inches
Yards
Fahrenheit
More than likely, you said the following things
• Gallon of milk.
• 65 miles per hour
• Quarter Pounder
• 48 inches
• Temperature in Fahrenheit
Copyright © 2010 Ryan P. Murphy
The countries colored in red are the ones that use
the Imperial System
Canada (sometimes)
The United States
Burma
Liberia
Copyright © 2010 Ryan P. Murphy
The Imperial System
LENGTH
Many units in the imperial
system are based on
measurements of the
human body.
The units for the length of THE IMPERIAL
SYSTEM is based on the following:
An inch represents the width of a thumb
Yard
the distance from the tip of the nose to the end of the
middle finger of the outstretched hand
Foot (12 inches)
originally the length of a human foot, although it has
evolved to be longer than most peoples feet.
Copyright © 2010 Ryan P. Murphy
Mile
A Roman unit, originally defined to be the length of 2000 steps of a
Roman legion.
THE IMPERIAL SYSTEM (Length) SUMMARY
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Converting between Imperial Units
Conversion factors
Copyright © 2010 Ryan P. Murphy
Convert 51 in. to:
i) Feet
ii) Feet and inches
A relationships between any quantities
can be expressed by CONVERSION
FACTORS
Copyright © 2010 Ryan P. Murphy
Convert 51 in. to:
i) Feet
ii) Feet and inches
Step 1: Look up the relationship between the units you are given
(inches) and you want to convert to (feet)
Step 2: Write 2 conversion factors for these units (inches and
feet)
Step 3: Choose a conversion factor which will allow you to cancel
units of a given quantity (inches in our case)
Step 4: Cancel, Multiply and Check the units
Copyright © 2010 Ryan P. Murphy
Convert 51 in. to:
i) Feet
ii) Feet and inches
Step 1: Look up the relationship between the units you are given
(inches) and you want to convert to (feet)
Copyright © 2010 Ryan P. Murphy
Convert 51 in. to:
i) Feet
ii) Feet and inches
Step 1: Look up the relationship between the units you are given
(inches) and you want to convert to (feet)
Step 2: Write 2 conversion factors for these units (inches and
feet)
Step 3: Choose a conversion factor which will allow you to cancel
units of a given quantity (inches in our case)
Copyright © 2010 Ryan P. Murphy
Convert 51 in. to:
i) Feet
ii) Feet and inches
Step 4: Cancel, Multiply and Check the units
Copyright © 2010 Ryan P. Murphy
POWERPOINT PRACTICE PROBLEM
Convert 62 in. to appropriate units
Convert 62 in. to:
i) Yards
ii) Feet and inches
iii) Yards, feet, and inches
Step 1: Look up the relationship between the units you are
given and you want to convert to
Step 2: Write 2 conversion factors for these units
Step 3: Choose a conversion factor which will allow you to
cancel units of a given quantity
Step 4: Cancel, Multiply and Check the units
Copyright © 2010 Ryan P. Murphy
Solving a Problem Involving Converting
Between Imperial Units
Anne is framing a picture. The perimeter of the framed picture will be 136 in.
a) What will be the perimeter of the framed picture in feet and inches?
b) The framing material is sold by the foot. It costs $1.89/ft. What will be the
cost of material before taxes?
Copyright © 2010 Ryan P. Murphy
Anne is framing a picture. The perimeter of the framed picture will be 136 in.
a) What will be the perimeter of the framed picture in feet and inches?
b) The framing material is sold by the foot. It costs $1.89/ft. What will be the
cost of material before taxes?
Copyright © 2010 Ryan P. Murphy
POWERPOINT PRACTICE PROBLEM
Ben buys baseboard for a bedroom. The perimeter of the bedroom, excluding closets
and doorway, is 37 ft.
a) What length of baseboard is needed, in yards and feet?
b) The baseboard material is sold by the yard. It costs $5.99/yd. What is the cost of
material before taxes?
Copyright © 2010 Ryan P. Murphy
Solving a Problem Involving Scale Diagrams
Copyright © 2010 Ryan P. Murphy
Solving a Problem Involving Scale Diagrams
A map of Alaska has a scale of 1:4 750 000. The distanc eon the map between
𝟏𝟏
Paxson and the Canadian border is 3 in. What is this distance to the
nearest mile?
𝟏𝟔
The distance between Paxson
and the Canadian border is
approximately 276 mi.
Copyright © 2010 Ryan P. Murphy
1.1 HOMEWORK
O Pages: 11 – 12
O Problems: 3, 8, 10, 16
Homework Solution
1.
1 in 2/16 + 1 in + 1 in. 1/16 = 3 in 3/16
2.
Scale = 1 in : 85 mi. so,
•
3 3/16 · 85 = 270.9 = 271 miles
Copyright © 2010 Ryan P. Murphy
Homework Solution
1.
1 in 2/16 + 1 in + 1 in. 1/16 = 3 in 3/16
2.
Scale = 1 in : 85 mi. so,
•
3 3/16 · 85 = 270.9 = 271 miles
3.
Speed = 50 mi. per 1 hour
Time = distance/ speed
Time = 5.4 hr  2 DAY TRIP
4.
1 in 13/16 + 1 in. 6/16 = 3 in 3/16
It’s the same distance
Copyright © 2010 Ryan P. Murphy
Homework Solution
1 mm : 0.01 mm
35 cm
Copyright © 2010 Ryan P. Murphy
Homework Solution
2400 cm = 24 m
1 : 0.008
2000000 cm =
20 km
Copyright © 2010 Ryan P. Murphy