1. Squared and Cubed Conversion Factors

2. 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

3. ( ) ( ) ( ) ( ) 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

4. ( ) ( ) ( ) 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

5. 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

6. ( ) ( ) ( ) ( ) ( ) 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 =

7. 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

8. Convert to mm3.

9. 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