Hfcc Math Lab Nat 05 Conversions Using Dimensional Analysis Worksheet With Answer Key - 2011
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5HFCC Math Lab
NAT – 05
Dimensional Analysis
Dimensional Analysis is a simple method for changing from one unit of measure to another.
Can you answer these questions?
How many feet are in 3.5 yards?
How many yards are in 49 ft?
Did you ever get confused about whether to multiply or divide in these situations? Then Dimensional
Analysis is what you need to know!
Dimensional Analysis makes use of the fact that everyone knows from arithmetic, namely:
× =
Any number (or quantity)
1 the number (or the quantity)
× =
Stated another way,
a
1
a
× =
For example: 5 1 5
2
2
× =
1
3
3
×
=
3 yds
1 3yds
× =
7.25 mi 1 7.25 mi
Conclusion: Multiplying by 1 does not change the value of a number or quantity.
From your work with fractions, you know that the number 1 can take on many forms:
3
4
125
36
=
=
=
=
1
,
1
,
1
,
1
etc.
3
4
125
36
Or using the following conversion equations:
1 foot (ft) = 12 inches (in)
3 ft = 1 yard (yd)
5280 ft = 1 mile (mi)
We can think of the number 1 in the following ways:
1 ft
3 ft
5280 ft
=
=
=
1
1
1
12 in
1 yd
1 mi
12 in
1 yd
1 mi
=
=
=
1
1
1
1 ft
3 ft
5280 ft
NOTE: Fractions that are equal to 1 are called unit fractions.
a quantity
× =
=
a
1
a
and 1
We can use these two ideas,
, to convert from one unit to
an equivalent quantity
another.
Revised 5/2011
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