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10 Metric Conversions and Unit Analysis

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10

Metric Conversions

and

Unit Analysis

Very small

pm

picometer

x 103

x 103

nanometer

ηm

x 103

micrometer

μm

x 103

millimeter

mm

x 103

m

meter

x 103

km

kilometer

x 103

Mm

megameter

x 103

Gm

gegameter

terameter

Very big

Tm

You should also know

x 101

millimeter

mm

x 102

centimeter

cm

m

meter

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 x 103 m

1 Mm

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 10-6m

x 1 x 103mm

x 1 x 103μm

x 1 x 103nm

1 m

1 mm

1μm

=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

x1 m

1 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

x1 km

1 x 103 m

1 x 103 μm

1 x 103 mm

=5.88 x 10-1 km

5. Convert 65 m2 to mm2

65 m2

x 1 x 103

( )2

mm

2

2

1 m

= 6.5 x 107 mm2

6. Convert 875 mm3 to m3

875 mm3

x 1 m

3

3

( )3

mm

1 x 103

=8.75 x 10-7 m3