Transcript III. Unit Conversions

Dimensional Analysis
III. Also called the Factor-Label
Method for solving problems
I
II
III
A. SI Prefix Conversions
1. Find the difference between the
exponents of the two prefixes.
2. Move the decimal that many places.
To the left
or right?
A. SI Prefix Conversions
532 m
NUMBER
UNIT
0.532 km
= _______
=
NUMBER
UNIT
A. SI Prefix Conversions
move right
move left
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
A. SI Prefix Conversions
1) 20 cm =
0.2
______________
m
2) 0.032 L =
32
______________
mL
3) 45 m =
45,000
______________
nm
0.0805
4) 805 dm = ______________
km
B. Dimensional Analysis
 The “Factor-Label” Method=
 A method of using units (labels, dimensions) to
analyze and solve word problems
– Cancel out units (dimensions)!
g
cm 

g
3
cm
3
B. Dimensional Analysis

Steps:
1.
Identify the final units of the answer
(and necessary equalities)
2. Start by writing the given
(magnitude and dimension)
3. Cancel units using conversion factor equalities
(the numerator must equal denominator)
4. Multiply all top numbers & divide by each bottom
number.
(calculate the numbers!)
B. Dimensional Analysis
 Lining up conversion factors:
1 in = 2.54 cm
=1
2.54 cm 2.54 cm
1 in = 2.54 cm
1=
1 in
1 in
B. Dimensional Analysis
 How many milliliters are in 1.00 quart of
milk?
qt
mL
1.00 qt

1L
1000 mL
1.057 qt
1L
= 946 mL
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.
cm3
lb
1.5 lb 1 kg 1000 g 1 cm3
2.2 lb
1 kg
19.3 g
= 35 cm3
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
1L
1000 cm3
= 1.23 L
B. Dimensional Analysis
5) 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
B. Dimensional Analysis
6) Taft football needs 550 cm for a 1st
down. How many yards is this?
cm
550 cm
yd
1 in
1 ft 1 yd
2.54 cm 12 in 3 ft
= 6.0 yd
B. Dimensional Analysis
7) 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
1m
1 piece
1.5 cm
= 86 pieces