Unit Conversions-Take II
We use the Factor-Label method to convert
from one unit to another.
Key Idea:
-Use “conversion factors” to convert between
units. PAY ATTENTION TO UNITS so that
they cancel.
Units are your friends!!! They prevent
mistakes
1 km = 1000 m
(This is called an Equivalence Statement or Definition)
Any equivalence statement can be made into two
(conversion factors)
 1000 m = 1 km Note: both of these = 1
1 km
1000 m
Which one to use?
Depends on which direction you are trying
to go.
For example:
Convert 25 km to meters
Use the conversion factor that allows units
to cancel. Which one?
 1000 m or 1 km
1 km
1000 m
25 km x 1000 m = 25000 m (or 2.5 x 104 m)
1 km
given
conversion factor
Step-By-Step Method to Solving Problems.
Example: How many centimeters are there in 5.54
inches?
– Step 1: Find how many centimeters are
equal to one inch (Equivalence Statement).
1 inch = 2.54 cm or
2.54 cm = 1 inch
Step 2:
Turn the statement into a “conversion factor”
1 inch
=
1 or
2.54 cm
2.54
cm
= 1
1 inch
Step 3: Multiply the given by the conversion factor
which will allow the unit to cancel out.
5.54 inch X 2.54 cm = 14.1 cm
1 inch
given
conversion factor
Step 4: Check your sig figs and don’t forget units!
5.54 inch X 2.54 cm = 14.1 cm
1 inch
Three sig figs
Ex #2. How many kilometers is the
26.2 mile marathon?
Definition: 1 mi = 1.6093 km or
1 km = .62137 mi
26.2 mi x 1.6093 km = 42.2km
1 mi
given
conversion factor
You can do more than one conversion at a time.
Example: How many inches in 4.2 meters?
Definitions: 1 meter = 100 cm
1 inch = 2.54 cm
Set up:
4.2 meters X 100 cm X
1 meter
given
conversion
factor
1 inch = ???
2.54 cm
conversion
factor
Top and Bottom Conversions:
Mr Clauson’s Durango gets 7.2 km/L of gas.
How many miles per gallon is that?
Logic: Need to go from km mi on top, and from L to
gal on the bottom.
1 mi = 1.6093 km;
1 gal = 3.7854 L
7.2 km x 1mi
x 3.7854 L =
1L
1.6093 km 1 gal
Are the Sig Figs right?
NO!! 17 mpg
Another Top and Bottom example:
This year in physics, the fastest baseball
throw was 39.8 m/sec. What is the speed
in miles/hour?
• Logic: Need to go from m mi on top, and
from sec to hr on the bottom.
1 m = 3.28 ft; 1mi = 5280 ft; 1 hr = 60 min;
1 min = 60 sec
Doing Area Conversions
Use the conversion factors, but square them!!
Example: How many square feet in 3.3 square
yards?
The linear conversion factor
1 yard = 3 feet
Has to be squared!
3.3 yd2 X 3 ft X 3 ft = 3.3 yd2 x 3ft
1 yd 1 yd
1 yd
2
=
Answer = 29.7 sq ft = 3.0x101 sq ft (sig figs!)
Doing Volume Conversions
Use the conversion factors, but cube them!!
Example: How many cubic meters in 357 cm3?
The linear conversion factor
1 m = 100 cm
Has to be cubed!
3.57 cm3
X
1m
100 cm
X
1m
X
100 cm
1m
=
3.57 cm3 x
100cm
Answer = 3.57x10-6 cubic meters
1m
100 cm
3
Homework
• Paddy’s Pool Procedure (Your individual
best!)
• Conversion WS #3
Learning Check
A Nalgene water
bottle holds 1000
cm3 of dihydrogen
monoxide (H2O).
How many cubic
decimeters is
that?
Solution
1000 cm3
(
3
)
1 dm
10 cm
= 1 dm3
So, a dm3 is the same as a Liter !
A cm3 is the same as a milliliter.