10Metric Conversions

and Unit Analysis

pm

μm

ηm

m

mm

km

Tm

Mm

Gm x 103

picometer

nanometer

meter

x 103

x 103micrometer

megameter

kilometer

gegameter

millimeter

x 103

x 103

x 103

x 103

x 103

Very small

terameterVery big

You should also know

mm

m

cm

meter

x 101millimeter

centimeter x 102

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 kmx 1 x 103 km

1 Mm1.23 x 1012 Mm

1. Convert 1.23 x 1012 Mm to m- you can only convert by 103 in any one step!

x 1 x 103 m

Write the starting number and units

Multiply with 1 Mm on the bottom and 103 km on top

Do the math and round off to three sig figs

Mutiply with 1 km on the bottom and 103 m on top

= 1.23 x 1018 m

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 nm x 1 x 103 μm1 m 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 x 1 mm x 1 m1 x 103 nm 1 x 103 μm 1 x 103 mm

= 6.5 x 10-3 m

4. Convert 5.88 x 108 μm to km

5.88 x 108 μm x 1 mm x 1 m x 1 km1 x 103 μm 1 x 103 mm 1 x 103 m

= 5.88 x 10-1 km

5. Convert 65 m2 to mm2

( )2 mm 2

1 m2

x 1 x 103

= 6.5 x 107 mm2

65 m2

6. Convert 875 mm3 to m3

875 mm3 x 1 m

1 x 103 mm

3

3 ( )3

= 8.75 x 10-7 m3