10
Metric Conversions
and
Unit Analysis
Very small
pm
picometer
x 103
ηm
nanometer
x 103
μm
micrometer
mm
millimeter
x 103
x 103
meter
x 103
km
kilometer
x 103
Mm
megameter
x 103
Gm
gegameter
x 103
Tm
terameter
m
Very big
You should also know
millimeter
x 101
cm
centimeter
x 102
m
meter
mm
We are going to use unit analysis to do some metric conversions.
The main purpose of this is to learn unit analysis and secondly learn
about metric conversions.
To facilitate this you are only allowed to convert by 103 x per conversion.
Please do the same in your workbook. We use unit analysis as our main
calculation tool in Chemistry 11 and Chemistry 12.
Learn it well and you will do awesome in chemistry.
1. Convert 1.23 x 1012 Mm to m- you can only convert by 103 in any
one step!
1.23 x 1012 Mm x
=
1 x 103 km x
1 Mm
1 x 103 m
1 km
1.23 x 1018 m
Write the starting number and units
Multiply with 1 Mm on the bottom and 103 km on top
Mutiply with 1 km on the bottom and 103 m on top
Do the math and round off to three sig figs
2. Convert 6.5 x 10-6 m to nm- you can only convert by 103 in any one
step!
6.5 x 10-6 m
=
x 1 x 103 mm x 1 x 103 μm x 1 x 103 nm
1m
1 mm
1 μm
6.5 x 103 nm
3. Convert 6.5 x 106 nm to m- you can only convert by 103 in any one
step!
6.5 x 106 nm
=
x
1
μm
1 x 103 nm
6.5 x 10-3 m
x
1 mm
x
1 x 103 μm
1m
1 x 103 mm
4. Convert 5.88 x 108 μm to km
5.88 x 108 μm x 1
mm x 1 m
x
1 x 103 μm
1 x 103 mm
=
5.88 x 10-1 km
1 km
1 x 103 m
5. Convert 65 m2 to mm2
65 m2
=
x
( 1 x 103 )2 mm 2
2
1m
6.5 x 107 mm2
6. Convert 875 mm3 to m3
875 mm3
x
= 8.75 x 10-7 m3
1 m3
( 1 x 103 )3 mm
3