Unit Conversions “Using Dimensional Analysis”

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SL#14 How to use Conversion Factors (a.k.a. Dimensional Analysis)

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Presentation transcript:

Unit Conversions “Using Dimensional Analysis” We call this the “Picket Fence” method to convert units (the book calls it the Factor-Label method to convert from one unit to another. (pg. 130-134 in text) Units are our friends, really!

Is a method to convert units. “Picket Fence” Is a method to convert units. Examples include: Feet Inches Kilometers  Meters Kilograms  Grams

Principle Behind Dimensional Analysis You can multiply anything by 1 without changing the physical meaning.

How Do We Multiply By 1 If the same thing is on the top and the bottom of a fraction,  = 1 Then they cancel out… and become 1

All Equalities = 1 Any time you put two things that are equal to each other 1000g = 1kg On top and on bottom 1000 g --------- = 1 1 kg Then they cancel out… and become 1.

All Equalities = 1 It doesn’t matter which is on top and which is on bottom. 1000 g 1 kg --------- = 1 or --------- = 1 1 kg 1000 g Both cancel out… and become 1.

1 km = 1000 m (A metric equality) Any equality can be written two ways (conversion factors) 1000 m = 1 km = 1 1 km 1000 m Which one to use? Depends on which direction you are trying to go.

The Rules Write down “given” + unit Draw a horizontal & vertical line “picket fence” Write “wanted” / “given” on the fence Enter proper #s for “wanted units & “given” units Cancel units & do the math

“given” unit = “want” unit For example: Convert 25 km to meters Use the conversion factor that allows units to cancel. 1000 m or 1 km 1 km 1000 m “given” unit = “want” unit picket fence

For example: Convert 25 km to meters (m) Use the conversion factor that allows units to cancel. 1000 m 1 km 25 km 1000 m = 25000 m (or 2.5 x 104 m) Just a little Scientific notation picket fence “given” conversion ‘want’ factor

Example: Convert 12.5 g to kg (1) 12.5 g 1 kg = 0.0125 kg 1000g (4) (3) (2) (5) Don’t forget the units

See what happens without UNITS?!?!?

Here’s a lady that talks really fast explaining dimensional analysis. Dimensional Analysis Video Demostration

Try: 18.2 km to m

Try: How many centimeters are there in 5.54 inches?