Conversion Factors
Supplement for Physical Science Chemistry
Module 2 – Metric Conversions
1. Table of Metric Prefixes
Multiplication Factor
Prefix
Symbol
1,000,000,000 = 109
1,000,000 = 106
1,000 = 103
100 = 102
10 = 101
1=1
0.1 = 10-1
0.01 = 10-2
0.001 = 10-3
0.000001 = 10-6
0.000000001 = 10-9
giga
mega
kilo
hecto
deca
G
M
k
h
da
deci
centi
milli
micro
nano
d
c
m
µ
n
Metric / English Equivalents
1 kilogram = 2.205 pounds
1 gram = 0.00220462262 pounds
1 liter = 1.0566882 quarts
1 meter = 1.0936133 yards
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2. Metric Conversions: Moving Decimal Places
When converting from
larger units to smaller units, move
the decimal point to the right.
Conversion Factors
larger
units
For example, how many meters are
contained in 3 kilometers?
3 km = 3. = 3 _ _ _ . = 3000 m
More small parts (meters) are needed to
make up the number (3) of larger things
(kilometers), so the decimal point is moved
to the right to make the actual number larger
(3000).
For example, how many millimeters
are contained in 5 meters?
5 m = 5. = 5_ _ . = 500 cm
1 kilo = 1,000 base units
Move 3
decimal
places
to go
from base
unit to
kilo
Move 1
decimal
place to
go from
centi to
deci
When converting from
smaller units to larger units, move
the decimal point to the left.
For example, how many kilometers
are contained in 3 meters?
3 m = 3. =
1 giga = 1,000,000,000 base
units
1 mega = 1,000,000 base units
smaller
units
1 hecto = 100 base units
1 deca = 10 base units
(base unit)
1 deci = 0.1 base units
~ or ~
10 deci = 1 base unit
1 centi = 0.01 base units
~ or ~
100 centi = 1 base unit
1 milli = 0.001 base units
~ or ~
1,000 milli = 1 base unit
1 micro = 0.000001 base units
~ or ~
1,000,000 micro = 1 base unit
1 nano = 0.000000001 base units
~ or ~
1,000,000,000 nano = 1 base unit
. _ _ 3 = .003 km
Fewer large parts (kilometers) are needed to
make up the number (3) of smaller things
(meters), so the decimal point is moved to
the left to make the actual number smaller
(.003).
For example, how many decimeters
are contained in 5 centimeters?
5 cm = 5. = . _ 5 = .05 dm
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3. Metric Conversion: Using Conversion Factors
For Example: How many meters are contained in 50 yards?
Units Needed
Original
Conversion Factor: 1 meter = 1.0936133 yards
Original
X
Conversion Factor =
Units Needed
… set up the Conversion Factor so the units we don’t want cancel out …
50 yards
X
1 meter
= ? meters
1.0936133 yards
… Multiply …
(50 yards)(1 meter)
1.0936133 yards
= ? meters
… Cancelling Units …
(50 yards)(1 meter)
1.0936133 yards
= ? meters
… Solving the Problem …
(50 )(1 meter)
1.0936133
= 45.712 meters
How many meters are contained in 50 yards? Answer: 45.712 meters
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