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Understand how to use the metric system to
measure in science.
Understand how to convert units.
Understand why we need to convert units.
Base Units
Time – second (s)
Length – meter (m)
Mass – gram (g)
Volume – Liter (L)
Temperature – Kelvin (K)
Amount of a substance – mole (mol)
Electric Current – ampere (A)
Luminous intensity – candela (cd)
Derived Units (define)
Volume – cubic decimeter (dm3) or liter (L)
Density – kilograms/Liters (kg/L)
Speed – meters/second (m/s)
There are many more derived units
Larger than the base unit
Giga (G)
means 1,000,000,000
Mega (M)
means 1,000,000
Kilo (k)
means 1,000
Hecto (h)
means 100
Deca (da)
means 10
1 x 109 m = 1 Gm
1 x 106 g = 1 Mg
1 x 103 L = 1 kL
1 x 102 m = 1 hm
1 x 101 g = 1 dag
Smaller than the base unit
deci (d)
means 1/10
1 g = 1 x 101 dg
centi (c)
means 1/100
1 L = 1 x 102 cL
milli (m)
means 1/1,000
1 m = 1 x 103 mm
Smaller than the base unit
micro ()
means 1/1,000,000
1 g = 1 x 106 g
nano (n)
means 1/1,000,000,000
1 L = 1 x 109 nL
Angstrom (Å)
1 m = 1 x 1010 Å
means 1/10,000,000,000
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A fraction
Will always have the base unit in the fraction
(meter, liter, or gram)
Will always have the number “1” with the
larger valued prefix
Fraction can be “flipped” depending on which
unit you are trying to “factor” out and cancel
1 step problem
Example – How many grams are in 3.42 kg?
1.
Write down your known
3.42 kg
Example – How many grams are in 3.42 kg?
2.
Write down the conversion that involves
your known unit on bottom and the unit you
want to go to on top.
3.42 kg x ______g
kg
Example – How many grams are in 3.42 kg?
3. Give the larger prefix value a “one”
4. The other gets the value of the prefix.
3.42 kg
1000 g
1 kg
5. Cancel out units and solve.
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Remember if you have the same unit on top
and on bottom, they cancel out.
3.42 kg x 1000 g =3420 g
1 kg
How many Liters are in 1.5 x 106 nL?
1.5 x 106 nL
1L
1 x 109 nL
= 1.5 x 10-3 L
How many milligrams are in 260 grams?
260 g x
1000 mg
1g
= 260,000mg
Mystery of Orbiter Crash Solved
By Kathy Sawyer
Washington Post Staff Writer
Friday, October 1, 1999; Page A1
NASA's Mars Climate Orbiter was lost in space last
week because engineers failed to make a simple
conversion from English units to metric, an
embarrassing lapse that sent the $125 million craft
fatally close to the Martian surface, investigators
said yesterday. Officials are scrambling to
determine whether a similar error is buried in the
computer files of two other spacecraft currently
cruising through space: the Mars Polar Lander,
scheduled to hit the Martian surface on Dec. 3, and
the Stardust craft bound for a comet.
It now appears the error had affected the
orbiter mission from its launching almost 10
months and 416 million miles before its
Sept. 23 failure. And yet the problem was
never caught and corrected by the system of
checks and balances at the Jet Propulsion
Laboratory (JPL) in California, which manages
this and numerous other interplanetary
missions for NASA.
Example – How many milligrams are in
3.42 kg?
1.
Map out your strategy . Write the unit you
are starting with, the base unit you are
going to, and the unit you want to end with.
kg  g  mg
Start
base
final
Example – How many milligrams are in 3.42 kg?
2. Write down your known
3.42 kg
3.
Write down the first conversion. Remember,
the conversion that involves your known
unit on bottom and the base unit on top.
3.42 kg 1000 g
1 kg
4. Add the second conversion. Remember, the
conversion that involves your base unit on
bottom and the unit you want to go to on
top.
3.42 kg 1000 g
1 kg
1000 mg
1g
5. Cancel out units and solve.
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Remember if you have the same unit on top
and on bottom, they cancel out.
3.42 kg 1000 g 1000 mg
1 kg
1g
= 3.42 x 106 mg
How many milligrams are in 260
kilograms?
kg  g  mg
How many milligrams are in 260
kilograms?
kg  g  mg
260 kg
1000 g
1kg
1000 mg
1g
= 2.6 x 108 mg
How many megameters are in 50
Angstroms?
How many megameters are in 50
Angstroms?
Å  m  Mm
50 Å
1m
1 x 1010Å
1Mm
1 x 106m
= 5 x 10-15 Mm
Length
2.54 cm = 1 in
Mass
454 g = 1 lb
Volume
1 L = 1.06 qt
Some English to Metric Calculations will have
multiple steps.
Ex. How many ft are in 240 nm?
1.
Map out your strategy . Write the unit you
are starting with, the bridge between the
two systems, and the unit you want to end
with.
nm  m  cm  in  ft
Start
base
bridge finish
Example – How many ft are in 240 nm?
1.
Write down your known
240 nm
2.
Write down the first conversion. Remember,
the conversion that involves your known
unit on bottom and the base unit on top.
240 nm
1 m
1 x 109 nm
3.
Add the other conversions.
240 nm
1m
100 cm
1 x 109 nm 1m
1 in
1 ft =
2.54 cm 12 in
4. Cancel out units and solve.
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Remember if you have the same unit on top
and on bottom, they cancel out.
240 nm
=
1m
1 x 109 nm
100 cm
1m
= 7.9 x 10-7 ft
1 in
2.54 cm
1 ft
12 in
How many milligrams are in 12 ounces?
oz  lb  g  mg
How many milligrams are in 12 ounces?
oz  lb  g  mg
12 oz
1 lb
16 oz
454 g
1 lb
1000mg
1g
= 3.4 x 105 mg
How many miles are in 17.0 km?
How many miles are in 17.0 km?
km  m  cm  in  ft  mi
17.0 km 1000 m 100cm
mi
1km
1m
5280 ft
= 10.6 mi
1in
1 ft
2.54 cm 12 in
1
Example – Ex. Convert 146 km/h to m/s.
1.
Write down your known
146 km
h
2.
Write down the conversions for the top unit.
146 km
h
1 x 103 m
1 km
3.
Add the conversions for the bottom unit.
146 km
hr
1 x 103 m 1 hr
1 km
60 min
1 min
60 s
=
4. Cancel out units and solve.
 Remember if you have the same unit on top and on
bottom, they cancel out.
146 km
hr
1 x 103 m 1 hr
1 km
60 min
1 min
60 s
40.6 m/s
=
How many yards per minute are in 52.6 hm/s?