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Dimensional Analysis or the Factor Label Method

(single unit conversion)

 

 

Video Examples

How many cm are in 2 miles?

Given:   1 mile= 5,280 ft         1 ft= 12 in            1 in= 2.54 cm

How many seconds are in 1 year? (non-leap year)

Dimensional Analysis or the Factor Label Method Explained

Many, if not most, parameters and measurements in the physical sciences and engineering are expressed as a numerical quantity and a corresponding dimensional unit; for example: 1000 kg/m, 100 kPa/bar, 50 miles per hour, 1000 Btu/lb. Converting from one dimensional unit to another is often somewhat complex and being able to perform such conversions is an important skill to acquire.

The method is based on quantities that can be defined as equalities.

 

Therefore, from any equality two fractions can be formed, each equal to one.In terms of measured quantities:

As a rule of thumb your problem set up should look like this:

Sometimes you will need to multiply by more than one ratio to get to your desired units, you can do this by using linking units. Your setup will look like this:

Important Conversion Factors

60 seconds = 1 minute
60 minutes = 1 hour
1 mile = 5280 feet
1 foot = 12 inches
2.54 centimeters = 1 inch
100 centimeters = 1 meter

Simple Example

 How many wheels on 350 Ford pickups (use the equality 1 pickup = 4 tires)

-the starting units are pickups, the ending units need to be wheels.

Try these

1. How many centimeters are in 6.00 inches?

2. If it takes 2.5 minutes to complete a task, what is that same length of time in seconds?

3. Express 24.0 cm in inches.

4. If a container of water absorbs 3.4 cal of heat, what is the amount of energy absorbed (in joules)?

5. How many seconds are in 2.0 years?

ANSWERS

1
2
3
4
5

 

Advanced Factor Label -(Double Unit Conversions)

Cancelling Units From

http://www.purplemath.com/modules/units.htm

AP Chemistry- Cubic Unit Factor Label Conversions

Sometimes it is necessary from one cubic unit another convert cubic unit.

Example -Convert 19.32g/cm3 to kg/m3

 

You have to cube the whole factor to make it into a volume factor.

 

Metric System  Metric conversions  Accuracy Precision Dimensional Analysis Scientific Notation  Significant Figures  Significant Figures in Calculations Rounding using Significant Figures Density

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