# 5.4 Dimensional Analysis

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```					           5.4 Dimensional Analysis
0011 0010 1010 1101 0001 0100 1011

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5.4 Dimensional Analysis
Process of converting from one unit to another
0011 0010 1010 1101 0001 0100 1011

Conversion factor: a ratio of two quantities that are
equal but use different units.

Example: To convert inches to feet
Use the ratio 1 ft as a conversion factor.   1
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12 in.
Common Conversions
• There are 5280 feet in 1 mile
• There are 60 seconds in 1 minute
0011 0010 1010 1101 0001 0100 1011
• There are 60 minutes in 1 hour
• There are 12 inches in 1 foot
• There are 3 feet in 1 yard

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• There are 1760 yards in 1 mile
• There are 1000 meters in 1 kilometer
• There are 4 quarts in 1 gallon

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• There are 52 weeks in a year
• There are 7 days in a week
• There are 24 hours in 1 day
• There are 16 ounces in a pound
• There are 1000 grams in a kilogram
Multiplying by a conversion factor is like
multiplying by 1.

1 ft = 12 in.
0011 0010 1010 1101 0001 0100 1011

= 1 ft = 1
12 in.  12 in.   1 ft

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A car traveled 60 miles on a
road in 2 hours. Find this rate
hours
in feet 0001 second.
0011 0010 1010 1101 per0100 1011
second
Conversion factor
5,280 ft
• Feet to miles     1 mi

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• Hours to minutes       1 hr
60 min
1 min

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• Minutes to seconds
60 sec
1. Multiply by each conversion factor separately
or
2. Simplify the problem and multiply by several
conversion factors at once.
A car traveled 60 miles on a road in 2
hours. Find this rate in feet per second.
1. Multiply by each conversion factor separately
Miles Feet
0011 0010 1010 1101 0001 0100 1011

60 mi  5,280 ft  316,800 ft              2      158,400 ft
                                 2    
2 hr   1 mi       2 hr                            1 hr

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Hours     Minutes

158,400 ft  1 hr  158,400 ft  60   2,640 ft

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1 hr
          60 min  60   1 mim
     
 60 min 
Minutes      Seconds
2,640 ft   1 min   2,640 ft           60 

44 ft
 60 sec                      60 
     
1 min               60 sec                         1 sec
2. Simplify the problem and multiply by several conversion
factors at once.
60 mi 2  30 mi
0011 0010 1010 1101 0001 0100 1011
2 hr 2     1 hr

30 mi   5280 ft   1 hr   1 min 
 1 mi            
  60 min   60 sec 
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1 hr                                 

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30  5280 ft 158,400 ft 44 ft

60  60 sec 3600 sec  1 sec

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