Transcript Slide 1

Conversion Factors
&
Dimensional Analysis
2.2
Pounds
1000g
A conversion factor:
1. Is used to convert a measured quantity
to a different unit of measure without
changing the amount.
2. Is a ratio of two equal values with
different units.
3. Always has a ratio that equals 1.
Dimensional Analysis
A system of using the units of
quantities to guide the mathematical
operations.
Step 1. Show what you are given on the left, and what
units you want on the right.
Step 2. Insert the required conversion factors to change
between units.
In this case we need only one conversion factor, and we
show it as the fraction, 1hr/60min. We put minutes on the
bottom so that they will cancel out with the minutes on the top
of the given.
Step 3. Cancel units where you can, and solve the math.
prefix
sym
bol
value
yotta
Y
1024
zetta
Z
1021
exa
E
1018
peta
P
1015
tera
T
1012
giga
G
109
1 000 000 000 U.S. billion
mega
M
106
1 000 000 million
kilo
k
103
1 000 thousand
hecto
h
102
100 hundred
deca
da
101
10 ten
deci
d
100
10-1
1 one
0.1 Tenth
centi
c
10-2
0.01 Hundredth
milli
m
10-3
0.001 Thousandth
micro
u
10-6
0.000 001 Millionth
nano
n
10-9
0.000 000 001 U.S. billionth
pico
p
10-12
femto
f
10-15
expanded value
English name
1 000 000 000 000 000 000 000 000 U.S. septillion; U.K. quadrillion
1 000 000 000 000 000 000 000 U.S. sextillion
1 000 000 000 000 000 000 U.S. quintillion; U.K. trillion
1 000 000 000 000 000 U.S. quadrillion
1 000 000 000 000 U.S. trillion; U.K. billion
0.000 000 000 001 U.S. trillionth; U.K. billionth
0.000 000 000 000 001 U.S. quadrillionth
deci
d
10-1
0.1
tenth
centi
c
10-2
0.01
hundredth
milli
m
10-3
0.001
thousandth
micro
u
10-6
0.000 001
millionth
nano
n
10-9
0.000 000 001
U.S. billionth
pico
p
10-12
0.000 000 000 001
U.S. trillionth; U.K. billionth
femto
f
10-15
0.000 000 000 000 001
U.S. quadrillionth
atto
a
10-18
0.000 000 000 000 000 001
U.S. quintillionth; U.K.
trillionth
zepto
z
10-21
0.000 000 000 000 000 000 001
U.S. sextillionth
yocto
y
10-24
0.000 000 000 000 000 000 000 001
U.S. septillionth; U.K.
quadrillionth
Derived Units and Density
Some units describe one base
measurement:
length
m
mass
g
1 kg = 1000 g
1 kg = 1 X 103 g
1 g = 0.001 kg
1 g = 1 X 10-3 kg
1 g = 10-3 kg
1 kg = 103 g
1 mg = 0.001 g
1 mg = 1 X 10-3 g
1 g = 1000 mg
1 g = 1 X 103 mg
1 g = 103 mg
1 mg = 10-3 g
1 ng = 0.000000001 g
1 ng = 1 X 10-9 g
1 g = 1000000000 ng
1 g = 1 X 109 ng
1 ng = 10-9 g
1 g = 109 ng
Derived units describe a
combination of base
measurements:
Area = m x m = m2
length x width x height
Volume = cm x cm x cm= cm3
= ml
Density is a derived unit:
Density = mass/volume
= g/cm3
= g/ml