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# Dimensional Analysis

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## David Ely

on 29 October 2015

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#### Transcript of Dimensional Analysis

Dimensional Analysis
What do we know?
In measuring length, we use a variety of different units.
In the United States, the system of measurement we generally use is called the English system.
An example unit would be an inch. What are some others?
Tougher right?
Often times, we can just use memories of basic conversion ratios (12 in. = 1 ft, 3 ft = 1 yd, 36 in. = 1 yd)
But what do we do when it's not as simple?
We use
Dimensional Analysis
Through the use of
unit fractions
, we can convert from one unit of measurement to another.
So how many feet are in two yards?
We need to eliminate the yards and introduce feet.

2 yd = 2 yd x 3 ft = 2 x 3 ft = 6 ft
1 1 yd
What else do (might) we know?
How many inches make up a foot?
How many feet are in a yard?
Bonus: How many feet are in a mile?
Easy enough right?? Let's switch it up a bit...
If three feet make up a yard, how many inches are in a yard?
If there are 12 inches in a foot, how many inches are in 10 feet?
How many feet are in two yards?
What makes a
Unit Fraction
?
Two rules:
(1) The numerator and denominator contain different units
(2) The value of the unit fraction is 1
Unit Fractions
12 in 1 ft 3 ft 1 yd
1 ft 12 in 1 yd 3 ft

5280 ft 1 mi
1 mi 5280 ft
The numerator and denominator are equal measures, making the value of the fraction 1.
Dimensional Analysis
To convert a measurement to a different unit:
Multiply by a unit fraction (or fractions if needed)
Place the unit(s) you wish to eliminate in the denominator(s); and the units you wish to introduce in the numerator(s).
How many yards are in a mile?
1 mi = 1 mi x ft x yd
1 mi ft

=
David Ely, IV
General Mathematics 155
Phylicia Joy
October 29, 2015

PA Standards and Anchors:
PA Standard - 2.3.8.D: Perform conversions within the metric system and within the customary system.

Assessment Anchor - M8.B.1: Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement.

Any Questions???
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