Learning Objectives

The Metric System

The standard units of measurement in the metric system are...

time = second [s]

mass = gram [g]

length = meter [m]

volume = liter [L]

temperature = Kelvin [K] or Celsius (centigrade) [^oC]

These basic units are modified by the following prefixes...

kilo = 1000 times the unit [k]

1 kg = 1000 g (1 kilogram = 1000 grams)

deci = 0.1 times the unit [d]

1 dL = 0.1 L (1 deciliter = 1/10^th liter)

centi = 0.01 times the unit [c]

1 cm = 0.01 m (1 centimeter = 1/100^th meter)

milli = 0.001 times the unit [m]

1 ms = 0.001 s (1 millisecond = 1/1000^th second)

Dimensional Analysis

This is a method of problem solving that uses conversion factors to change the units of a measurement into different units.

When we convert an hour into minutes we merely remember that 1 hour equals 60 minutes and multiply the number of hours by 60. We rarely think about the units of minutes and hours since we frequently do this type of conversion. The conversion factor in this case is 60 minutes/1 hour. Try converting 0.4 hours to minutes using this factor. Now lets see what happens when we convert minutes to hours. The same conversion factor can be used but it must be inverted so the units come out correctly...1 hour/60 minutes. Try converting 240 minutes to hours using this new factor.

Note that it is very important that the denominator of the conversion factor must have the same units as the numerator of the previous term or the units will not cancel out. Think of the units as patterns that you are trying to match...like a game or puzzle.

Now that you have tried the game with patterns, let's try another game involving metric conversions.

Conversions can be fairly complicated and keeping track of the units is critical in order to arrive at the correct numerical answer because it is easy to be confused and divide when you should multiply.

In order to better appreciate this concept, try to convert 4 hours into seconds.

Problems

1. How many milligrams are present in 2 kilograms?

2. How many liters are in 25 milliliters?

3. How many decimeters are in 20,000 millimeters?

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