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The Metric System
Practice Problem 1:
Try completing the table below; the first row is done for you.
Meters (m)
If you’re unsure, try writing extra zeroes after the decimal point. If we aren’t
worried about showing precision, then 25400 cm means the same thing as
25400.00 cm:
254000.0 mm = 25400.00 cm = 254.000 m = .254000 km
The decimal point moves left as we convert into bigger units of
measurement! Here are a few memorization tricks:
There are 100 centimeters in a meter – just as there are 100 cents in a
Y2K was the year 2000. A 50k salary is $50,000 / year. So k means
1,000, and a km, or kilometer, is 1000 meters.
Milli- means 1/1000. There are 1000 millimeters in a meter – just as
there are 1000 years in a millennium. This one is slightly backwards, but
I’ve yet to find a better example.
Micro- means "tiny", so it's just 1/1,000,000th of a base unit. That is,
Practice Problem 2:
The metric system is consistent. Whether you're converting centigrams
into grams or centimeters into meters, the process is the same! Try completing
the table below containing an imaginary unit, the Dosh.
How many doshes is it?
.001 D
How many of
this unit in 1
1000 D
The Metric System
General Rules:
Consider the following problem:
How many meters is 32 centimeters?
When solving a conversion problem, the procedure is usually as follows:
1. Figure out what you are converting. Here, you are converting 32
centimeters into meters.
2. Examine the prefixes. A metric unit has two parts: a prefix (like kilo, centi,
etc), and a base unit (such as meter, gram, second, etc). Sometimes, the
prefix is absent. Here, our prefix is “centi-“. There are 100 centimeters in a
meter, just as there are 100 cents in a dollar.
3. Set up an equation to compare the units you are converting between:
100 cm = 1 m
4. Write down the measurement you are converting from: “34 cm”
5. Multiply it by a conversion factor you get from the equation you made in
part 3:
34 cm x ---------------- = ???
100 cm
Make sure the units cancel! Here, we put the “cm” on the bottom to cancel
with the “cm” in “34 cm!” This is important. If “100 cm” is on the top, we
get the wrong answer!
6. Finally, multiply or divide as is appropriate. Here, “1 m” is on the top –
multiplying by 1 doesn’t change our answer. “100 cm” is on the bottom, so
we divide 34 by 100. Cancel out the cm unit.
34 m
34 cm x ---------------- = -------------100 cm
7. To divide a number by 10, 100, 1000, etc, move the decimal point to the
left by the number of zeroes in the number you are dividing by. 34 cm has
a decimal point after the 4, because it is really “34.0 cm.” So it becomes
0.34 cm – we shifted the decimal left by two spaces.
The Metric System
8. To multiply a number by 10, 100, 1000, etc, move the decimal point to the
right by the number of zeroes in the factor you are multiplying by. For
example, to multiply 3.52 by 1000, we move the decimal three places right
and get 3520.
Some problems require multiple conversion steps. To solve these, you need to
be organized! Write down what you know (conversions, given facts, etc),
what you need to know, and then the steps to solve them. For additional help,
http://www.themetricsystem.info/ has a nice intro to the system and its units.
Temperature (a special case):
We measure temperature in degrees Celsius (°C), not degrees Fahrenheit!
This unit does not follow the rules for metric conversions! 0°C is the freezing
point of water, 25°C is roughly room temperature, and 100°C is the boiling point
of water. You will NOT be required to convert between °F and °C, but you should
know the differences between the two scales.
Practice Problems 3 - 6 : (Complete the following, showing your work)
3. Suppose a person has 720 cm of intestines. How many meters of intestines do
they have?
4. The average mass of a human brain is about 1.3 kg. How much is this in grams?
5. In school, you likely learned that the average human body temperature is
98.6°. Is this a Celsius temperature or a Fahrenheit temperature?
6. The lethal dose of caffeine is roughly 150 mg of caffeine for every kg of body
weight. I weigh about 70 kg. How much caffeine, in grams, would it take to kill