Transcript Slide 1

Measurement and
Dimensional Analysis
(DA)
 Dimensional



Analysis (DA)
One of the most powerful problem solving
techniques I can teach you.
Used to convert from one unit to another.
Generic form:
• Conversion Factors
• Conversion factor – a statement in which the
same thing is said in two different ways. Ex.
science = fun,
• 12 inches = 1 foot,
100 centimeters = 1
meter.
• When we use conversion factors in problem
solving (dimensional analysis), we are not
changing anything but the name given to the
number (unit).
• The numbers used in the conversion factor have
no effect on the number of sig figs in your
answer.
• Conversion Factors (cont.)
• What is any number or thing divided by
itself?
• Example:
•
1foot 12inches 1
12inches 1foot
• How many centimeters in 2 meters?
• Once you have the equalities you must pick
the one that will cancel out the units leaving
the desired units.
Try one
• 1. How many wheels on 350 Ford pickups (use
the equality 1 pickup = 4 wheel)
• -the starting units are pickups, the ending units
need to be wheels.
• Examples
• 1. How many kilometers are in 4.6 miles?
• 2. How many inches are in 345.8 cm?
• 3. How many ounces are 9.60 grams?
• Multiple Step Problems
• In the solution of these problems, more
than one conversion factor will be needed.
• Strategy: let the conversion factors show
you the way.
• How many centimeters are in 10.1 yards?
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:
How many inches in 1 meter
1 inch = 2.54 cm and 1 meter = 100 cm
1 inch
2.54 cm
Meter
1 meter
100 cm
CM
inches
Meter
CM
inches
1km
4 qt
4 pints
0.6 mi
1 gal
1 qt
5280ft
2.54cm
1 mi
1 inch
30 cm
1 ft
0.95 qt
1L
• Just plug in units
• 4. How many pints are in 17.10 gallons?
4. How many pints are in 17.10
gallons?
4 qt
4 pints
1 gal
1 qt
Quarts
gallons
gallons
pints
Quarts
pints
1km
4 qt
4 pints
0.6 mi
1 gal
1 qt
5280ft
2.54cm
1 mi
1 inch
• Just plug in units
• 5. How many miles are in 1.24
centimeters?
30 cm
1 ft
0.95 qt
1L
5. How many miles are in 1.24
centimeters?
1 Km
0.6km
1Mile
cm
100,000 cm
km
miles
cm
km
miles
1km
4 qt
0.6 mi
1 gal
30 cm
4 pints
1 ft
1 qt
5280ft
2.54cm
1 mi
1 inch
0.95 qt
1L
• Just plug in units
• 6. How many liters are in 90.21 pints?
6. How many liters are in 90.21 pints?
4 pints
0.95 qt
1L
1 qt
pints
quart
liters
pints
quart
liters