1. 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

2. Any equivalence statement can be made into two (conversion factors)
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 m
Which one to use?
Depends on which direction you are trying to go.

3. Use the conversion factor that allows units to cancel. Which one?
For example:
Convert 25 km to meters
Use the conversion factor that allows units to cancel. Which one?
 m or 1 km
1 km m
25 km x 1000 m = m (or 2.5 x 104 m)
1 km
given conversion factor

4. 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

5. given conversion factor
Step 2:
Turn the statement into a “conversion factor”
1 inch = 1 or cm = 1
2.54 cm inch
Step 3: Multiply the given by the conversion factor which will allow the unit to cancel out.
5.54 inch X cm = 14.1 cm
1 inch
given conversion factor

6. 5.54 inch X 2.54 cm = 14.1 cm Three sig figs
Step 4: Check your sig figs and don’t forget units!
5.54 inch X cm = 14.1 cm
1 inch
Three sig figs

7. Ex #2. How many kilometers is the 26.2 mile marathon?
Definition: 1 mi = km or
1 km = mi
26.2 mi x km = 42.2km
1 mi
given conversion factor

8. 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 inch = ???
1 meter cm
given conversion conversion
factor factor

9. 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 = km; 1 gal = L
7.2 km x 1mi x L =
1L km 1 gal
17.0 mpg
Are the Sig Figs right?
NO!! 17 mpg

10. 89.0 mph Big League speed! 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
89.0 mph Big League speed!

11. 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 2 =
1 yd yd yd
Answer = 29.7 sq ft = 3.0x101 sq ft (sig figs!)

12. 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 X 1m X 1m = cm3 x 1m 3
100 cm cm 100cm cm
Answer = 3.57x10-6 cubic meters

13. Homework Paddy’s Pool Procedure (Your individual best!)
Conversion WS #3

14. Learning Check
A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (H2O). How many cubic decimeters is that?

15. Solution
( )
1000 cm dm 3
10 cm
= 1 dm3
So, a dm3 is the same as a Liter !
A cm3 is the same as a milliliter.