1. Conversion Factors Dimensional Analysis Lots of Practice

2. A. Conversion Factors Example: 1 in. = 2.54 cm
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: in. = 2.54 cm
Factors: 1 in and cm
2.54 cm in.

3. A. Conversion Factors
If you know ONE conversion for each type of measurement, you can convert anything!
You must memorize and use these conversions
Mass: grams = 1 lb
2.2 lbs = 1 kg
Length: cm = 1 inch
1 mile = km
Volume: L = 1.06 quarts
1 L = 1000 mL
1 L = 1 dm3
1 mL = 1 cm3

4. A. Conversion Factors 1. Liters and mL 2. Hours and minutes
Write conversion factors that relate each of the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers

5. 1. Liters and mL 1 L = 1000 mL
1 L and mL
1000 mL L
2. hours and minutes 1 hr = 60 min
1 hr and min
60 min hr
3. meters and kilometers 1 km = 1000 m
1 km and m
1000 m km

6. B. Dimensional Analysis
The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out

7. B. Dimensional Analysis
Steps:
1. Identify starting & ending units.
2. Write down given/1
3. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number. Hit enter ONCE!
4. Check units & answer.

8. Example How many minutes in 2.5 hours? Conversion factor
2.5 hr x min = min
1 hr
cancel
UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

9. B. Dimensional Analysis
How many milliliters are in 1.00 quart of milk? qt mL
1.00 qt
1 L
1.057 qt
1000 mL
1 L
= 946 mL 

10. B. Dimensional Analysis
You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. lb
cm3
1.5 lb
1 kg
2.2 lb
1000 g
1 kg
1 cm3
19.3 g
= 35 cm3

11. B. Dimensional Analysis
How many liters of water would fill a container that measures 75.0 in3?
in3 L
75.0 in3
(2.54 cm)3
(1 in)3
1 L
1000 cm3
= 1.23 L

12. B. Dimensional Analysis
Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? cm in
8.0 cm
1 in
2.54 cm
= 3.2 in

13. B. Dimensional Analysis
Eastview football needs 550 cm for a 1st down. How many yards is this? cm yd
550 cm
1 in
2.54 cm
1 ft
12 in
1 yd
3 ft
= 6.0 yd

14. B. Dimensional Analysis
A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? cm
pieces
1.3 m
100 cm
1 m
1 piece
1.5 cm
= 86 pieces

15. Square/Cubic Units
Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!
Best way: Square or cube the ENITRE conversion factor
Example: Convert 4.3 cm3 to mm3
( )
4.3 cm mm 3
1 cm
4.3 cm mm3
13 cm3 =
= 4300 mm3

16. ( ) 1000 cm3 1 dm 3 10 cm = 1 dm3 So, a dm3 is the same as a Liter !
( )
= 1 dm3
So, a dm3 is the same as a Liter !
A cm3 is the same as a milliliter.