1. Conversion Factors and Unit Cancellation
Converting between two sets of units never changes the number of significant figures in a measurement. Remember, data are only as good as the original measurement, and no later manipulations can clean them up.

2. A physical quantity must include:
Number
+ Unit

3. Calculation Corner: Unit Conversion
1 foot = 12 inches

4. Calculation Corner: Unit Conversion
1 foot = 12 inches
1 foot
= 1
12 inches

5. Calculation Corner: Unit Conversion
1 foot = 12 inches
1 foot
= 1
12 inches
12 inches
= 1
1 foot

6. Calculation Corner: Unit Conversion
1 foot
12 inches
12 inches
1 foot
“Conversion factors”

7. Calculation Corner: Unit Conversion
1 foot
12 inches
12 inches
1 foot
“Conversion factors”
12 inches ( ) ( )
3 feet
= 36 inches
1 foot

8. ( ) ______ How many cm are in 1.32 meters? equality: 1 m = 100 cm
(or 0.01 m = 1 cm)
applicable conversion factors:
______
1 m
100 cm
______
1 m
100 cm or ( )
______
1 m
100 cm
132 cm
X cm = 1.32 m =
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.

9. Again, the units must cancel.
How many meters is 8.72 cm?
equality:
1 m = 100 cm
applicable conversion factors:
______
1 m
100 cm
______
1 m
100 cm or ( )
______
1 m
100 cm m
X m = 8.72 cm =
Again, the units must cancel.

10. Again, the units must cancel.
How many feet is inches?
equality:
1 ft = 12 in
applicable conversion factors:
______
1 ft
12 in
______
1 ft
12 in or ( )
____
1 ft
12 in
3.28 ft
X ft = in =
Again, the units must cancel.

11. ( ) ( ) ____ ______ How many kilometers is 15,000 decimeters? 10 dm
1 km
1.5 km
X km = 15,000 dm =

12. How many seconds is 4.38 days?
____ ( ) ( )
_____ ( )
____
24 h
1 d
1 h
60 min
1 min
60 s
X s = 4.38 d
378,432 s =
If we are accounting for significant figures, we would change this to…
3.78 x 105 s

13. Simple Math with Conversion Factors

14. Example Problem Measured dimensions of a rectangle:
length (L) = 9.70 cm
width (W) = 4.25 cm L W
Find area of rectangle.
A = L . W
= (9.70 cm)(4.25 cm) =
41.2 cm 2
. cm

15. ( ) ( ) ( ) ( ) Convert 41.2 cm2 to m2. ______ ______ ______ ______
X m2 = 41.2 cm2 =
0.412 m2
WRONG! =
0.412 cm.m
Recall that… 41.2 cm2 = 41.2 cm.cm ( )
______ ( )
______
X m2 = 41.2 cm.cm
100 cm
1 m
100 cm
1 m = m2 ( )
______
100 cm
1 m 2
X m2 = 41.2 cm2 = m2

16. ( ) ( ) ( ) Convert 41.2 cm2 to mm2. _____ _____ _____
Recall that… 41.2 cm2 = 41.2 cm.cm ( )
_____ ( )
_____
X mm2 = 41.2 cm.cm
1 cm
10 mm
1 cm
10 mm =
4,120 mm2 2 ( )
_____
1 cm
10 mm
X mm2 = 41.2 cm2 =
4,120 mm2

17. Measured dimensions of a rectangular solid:
Length = 15.2 cm
Width = 3.7 cm
Height = 8.6 cm H W
Find volume of solid. L
V = L . W . H
= (15.2 cm)(3.7 cm)(8.6 cm) =
480 cm 3

18. ( ) ( ) ( ) ( ) ( ) Convert to m3. _____ _____ _____ _____ _________
cm.cm.cm ( )
_____ ( )
_____ ( )
_____
100 cm
1 m
X m3 = 480 cm 3 2
100 cm
1 m
100 cm
1 m = or ( )
_____
100 cm
1 m 3
X m3 = 480 cm3 = m3 or
1 m cm ( )
_________ 3
X m3 = 480 cm3
4.80 x 10-4 m3 =

19. Convert to m3... Measured dimensions of a rectangular solid:
Length = 15.2 cm
Width = 3.7 cm
Height = 8.6 cm
0.152 m
0.037 m
0.086 m H W
Find volume of solid. L
V = L . W . H
= (0.152 m)(0.037 m)(0.086 m) = m 3

20. Convert to mm3.

21. By what factor do mm and cm differ? 10
100
By what factor do mm3 and cm3 differ?
1,000
1 cm = 10 mm
(1 cm)2 = (10 mm)2
1 cm2 = 100 mm2
(1 cm)3 = (10 mm)3
1 cm3 = 1000 mm3