Dimensional Analysis

1
Dimensional Analysis

• Dimensional Analysis The process of solving
  problems using conversion factors to convert
  measurements from givens to usable quantities.
• This process is sometimes called the Factor-Label
  method.

2
Dimensional Analysis

• The Factor-Label method requires us to use ratios
  equal to one.
• These are called ? Conversion Factors
• EX. 24 hrs 1 day
• 12 inches 1 foot

3
Dimensional Analysis

• The Main Rule ? Always deal with the units 1st
  then the numbers that match the units.
• Steps ?
• 1. Determine the Given or Starting Value.
• 2 Write the given (include units) as fraction
  (Place over 1)
• 3. Determine the unit that needs to be
  cancelled and place in the appropriate location
  in the factor- label table.
• 4. Use the matching conversion factor to get
  to desired units.
• 5. Repeat until you reach your answer with
  the correct units.

4
Dimensional Analysis

• Example
• 1. 20,000. ft _______________ miles

20,000 ft 1 mile
1 5,280 ft
3.7879 miles
5
Dimensional Analysis
2. How many days are in 1.00 seconds?
1.00 second 1 minute 1 hour 1 day
1 60 seconds 60 minutes 24 hours
1.16 x 10-5 days
6
Dimensional Analysis

• Conversion Factors
• English to Metric English to English
• 1 inch 2.54 cm 12 inch 1 ft
• 1 lbs 454 g 5280 ft 1 mile
• 2.2 lbs 1 kg 2000 lbs 1 ton
• 1 gal 3.79 L 16 oz 1 lbs
• 365.24 days 1 y 4 qts 1 gal
• 3600 s 1 hr 4 cups 2 pints 1 qt

7
Factor Label and the metric system

• Convert the following and turn in for homework
  using the factor label method. Using the
  conversion factors on the previous slide.
• 1. 100 cm ? ____m
• 2. 0.001 m ? ____mm
• 3. 1000 g ? ____ Mg
• 342 µs ? ____ s ? ____ hours
• 264.77 mL ? _____ kL
• 6 tons ? _____ kg
• 0.45 cups ? ____qts