Math 310
Section 11.1
Linear Measure
The English System (Length)
There are four major units for measuring length in
the English system:
 Inch
 Foot
 Yard
 Mile
The Metric System (Length)
There are four major units used in the metric
system for measuring length:
 Millimeter
 Centimeter
 Meter
 Kilometer
The Metric System Continued
Although the four just mentioned are the most
commonly used units, the metric system has
several more:
 Hectometer
 Dekameter
 Decimeter
Unit Conversions
English
English
12 inches
1 foot
3 feet
1 yard
5280 feet
1 mile
1760 yards
1 mile
Unit Conversions (Cont)
Metric
Metric
10 millimeters
1 centimeter
100 centimeters
1 meter
1000 meters
1 kilometer
Unit Conversions (Cont)
English
Metric
1 inch
Aprox. 2.54 centimeters
Dimensional Analysis
Dimensional analysis is a process for converting
between units. Similar to converting fractions,
the idea is that you multiply you starting value by
a fraction equal to one, thereby never actually
changing the value, just the representation.
Ex
Convert 2 feet to inches.
Convert 12 yards to inches.
Convert 4 miles to inches.
Convert 1 inch to miles.
Convert 3 kilometers to millimeters
Convert 1 foot to centimeters.
Convert 1 mile to kilometers.
Metric (distance function)
Def
A metric (distance function) is a function d(a, b)
that satisfies the following four criteria:
1. d(a, b) ≥ 0
2. d(a, b) = 0 means a = b
3. d(a, b) = d(b, a)
4. d(a, c) ≤ d(a, b) + d(b, c)
For Euclidean Geometry
1.
2.
3.
4.
AB ≥ 0
AB = 0 then A =B
AB = BA
AB + BC ≥ AC
Triangle Inequality
Def
The triangle inequality states that the sum of any
two sides of a triangle (3 pts in a plane) is
greater than the third side.
Ex
Ex
The perimeter of an isosceles triangle is 40, which
of the following could not be the base?




1
8
15
24
Perimeter
Def
The perimeter of a simple closed curve is the
length of the curve. For a polygon this is simple
the sum of the sides of the polygon.
Ex
Find the perimeter of the
following polygon.
1
2
4
4
1
5
20
3
Circumference
Def
A circumference is the perimeter of a circle.
Ex
Find the circumference
of the following circle
with the indicated radius.
3
6π
Arc Length
The length of an arc on a circle can be found with
the following formula:
l = (π·r·θ)/180
Where does this formula come from?
Ex
2
85°
Additional HW Problems


Covert 26 miles to kilometers.
Pg 748 prblm 19