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. Metric Conversions Kilo k Deci d Centi c Milli m Hecto h Deca da
Meter m
Gram g
Liter L
Deci d
Centi c
Milli m

3. Metric Equivalents mm daL kg dm cc L Millimeter Decaliter Kilogram
decimeter
cubic centimeter
cm3= mL
Liter
1000liter = m3

4. 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
(m to cm) 1.32 m =
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.

5. 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.

6. 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.

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

8. 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

9. Simple Math with Conversion Factors

10. 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

11. ( ) ( ) ( ) ( ) 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

12. ( ) ( ) ( ) 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

13. ( ) ( ) ( ) ( ) ( ) 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 =