Metric Conversions

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9 Metric Conversions and Unit Analysis
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nm 10-9 µm 10-6 mm 10-3
m 1 km 103 Mm 106 Gm
109
cm
3
nm 10-9 µm 10-6 mm 10-3
m 1 km 103 Mm 106 Gm
109 Larger Unit
cm
4
nanometer nm 10-9 micrometer µm
10-6 millimeter mm 10-3 meter m 1 k
ilometer km 103 megameter Mm
106 gigameter Gm 109 Larger Unit
cm
centimeter
dm
decimeter
hectometer
hm
5
nanogram ng 10-9 We can change the
base unit to grams microgram µg
10-6 milligram mg 10-3 gram g 1 kil
ogram kg 103 megagram Mg
106 gigagram Gg 109 Larger Unit
cg
centigram
dg
decimgram
hectogram
hg
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nanolitre nL 10-9 We can change the
base unit to litres microlitre µL
10-6 millilitre mL 10-3 litre L 1 k
ilolitre kL 103 megalitre ML
106 gigalitre GL 109 Larger Unit
cL
centilitre
dL
decilitre
hectolitre
hL
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Each mark on the nL 10-9 Line is a factor of
10 Complete the conversion µL 10-6 ? mL
? L mL 10-3 L 1 kL
103 ML 106 GL 109 Larger Unit
cL
dL
hL
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Each mark on the nL 10-9 Line is a factor of
10 1. Complete the conversion µL 10-6 ?
mL 1 L mL 10-3 Put a 1 with the
larger unit L 1 kL 103 ML
106 GL 109 Larger Unit
cL
dL
hL
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Each mark on the nL 10-9 Line is a factor of
10 1. Complete the conversion µL 10-6 ?
mL 1 L mL 10-3 mL is three spaces
or 103 L 1 kL 103 ML
106 GL 109 Larger Unit
cL
dL
hL
10
Each mark on the nL 10-9 Line is a factor of
10 1. Complete the conversion µL 10-6 1
x 103 mL 1 L mL 10-3 mL is three
spaces or 103 L 1 kL
103 ML 106 GL 109 Larger Unit
cL
dL
hL
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Each mark on the nL 10-9 Line is a factor of
10 2. Complete the conversion µL 10-6 ?
kL ?ML mL 10-3 Put a 1 with the
larger unit L 1 kL 103 ML
106 GL 109 Larger Unit
cL
dL
hL
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Each mark on the nL 10-9 Line is a factor of
10 2. Complete the conversion µL 10-6 ?
kL 1ML mL 10-3 kL is three spaces or
103 L 1 kL 103 ML
106 GL 109 Larger Unit
cL
dL
hL
13
Each mark on the nL 10-9 Line is a factor of
10 2. Complete the conversion µL 10-6 1
x 103 kL 1ML mL 10-3 mL is three
spaces or 103 L 1 kL
103 ML 106 GL 109 Larger Unit
cL
dL
hL
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1. Convert 1.23 x 1012 Mm to m- you can only
convert by 103 in any one step!
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1. Convert 1.23 x 1012 Mm to m- you can only
convert by 103 in any one step! 1. Write
the starting quantity with the unit.
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1. Convert 1.23 x 1012 Mm to m- you can only
convert by 103 in any one step! 1.23 x 1012
Mm 1. Write the starting quantity with the
unit.
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1. Convert 1.23 x 1012 Mm to m- you can only
convert by 103 in any one step! 1.23 x 1012
Mm 2. Multiply by a conversion factor where
the bottom of the factor has the same unit as
the starting one.
18
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 Mm 2. Multiply by a
conversion factor where the bottom of the factor
has the same unit as the starting one.
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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 1 Mm 2. Multiply by
a conversion factor where the bottom of the
factor has the same unit as the starting one.
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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 1 Mm Units cancel
converting to km! 2. Multiply by a conversion
factor where the bottom of the factor has the
same unit as the starting one.
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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
km 3. Repeat for km.
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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 3. Repeat for km.
23
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 Units cancel converting to m!
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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 Do the math and round off
to three sig figs like the starting number.
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2. Convert 6.5 x 10-6 m to nm- you can only
convert by 103 in any one step!
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2. Convert 6.5 x 10-6 m to nm- you can only
convert by 103 in any one step!
1. Write the starting quantity with the unit.
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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 1. Write the starting quantity with the
unit.
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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
2. Multiply by a conversion factor where
the bottom of the factor has the same unit as
the starting one.
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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 m
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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 1 m
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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 1 m 3. Repeat
for µm.
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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 m 1
mm 3. Repeat for µm.
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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 1
m 1 mm 3. Repeat for µm.
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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 1
m 1 mm 4. Repeat for nm.
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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 m 1 mm 1 µm Do the math and round off to
three sig figs like the starting number.
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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 1 m 1 mm 1 µm Do the math and
round off to three sig figs like the starting
number.
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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 1 m 1 mm 1 µm 6.5 x 103
nm Do the math and round off to three sig figs
like the starting number.
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3. Convert 6.5 x 106 nm to m- you can only
convert by 103 in any one step! 6.5 x 106
nm
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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
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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 1 x
103 nm 1 x 103 µm
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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 m
1 x 103 nm 1 x 103 µm 1 x 103
mm
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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 m
1 x 103 nm 1 x 103 µm 1 x 103
mm 6.5 x 10-3 m
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4. Convert 5.88 x 108 µm to km 5.88 x 108 µm
x 1 mm 1 x 103 µm
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4. Convert 5.88 x 108 µm to km 5.88 x 108 µm
x 1 mm x 1 m 1 x 103
µm 1 x 103 mm
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4. Convert 5.88 x 108 µm to km 5.88 x 108 µm
x 1 mm x 1 m x 1 km
1 x 103 µm 1 x 103 mm 1 x 103
m
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4. Convert 5.88 x 108 µm to km 5.88 x 108 µm
x 1 mm x 1 m x 1 km
1 x 103 µm 1 x 103 mm 1 x 103
m 5.88 x 10-1 km
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5. Convert 65 m2 to mm2
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5. Convert 65 m2 to mm2 65 m2
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5. Convert 65 m2 to mm2 65 m2 x 1
m
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5. Convert 65 m2 to mm2 65 m2 x 1 x
103 mm 1 m
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5. Convert 65 m2 to mm2 65 m2 x 1 x
103 mm2 1 m2
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5. Convert 65 m2 to mm2 65 m2 x (1 x
103)2 mm2 1 m2
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5. Convert 65 m2 to mm2 65 m2 x 1 x
106 mm2 1 m2
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5. Convert 65 m2 to mm2 65 m2 x 1 x
106 mm2 6.5 x 107 mm2 1 m2
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6. Convert 875 mm3 to m3
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6. Convert 875 mm3 to m3 875 mm3 x
1 m 1 x 103 mm
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6. Convert 875 mm3 to m3 875 mm3 x
1 m3 (1 x 103)3 mm3
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6. Convert 875 mm3 to m3 875 mm3 x
1 m3 1 x 109 mm3
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6. Convert 875 mm3 to m3 875 mm3 x
1 m3 8.75 x 10-7 m3 1 x 109
mm3