Recall that any measurement has two basic parts:
1) Value - indicates the magnitude of the measured quanitity as well as the level of precision with which the measurement was made.
2)  Unit(s) - tells the nature of the quantity and the scale on which it was measured.

In the U.S. we use:
1)  English System - for common measurements
2)  Metric System - for scientific work

Most of the world uses the metric system for all of its measurements because of its simplicity. It utilizes a system of base units and prefixes to create units of the appropiate size for the measurement being made. You intuitively do this when working with the English sysytem. For example, if you were asked, "How far is it from Rochester, Mn, to Chicago, Il?", you would probably answer in miles (362 miles). The mile is a large unit of length in the English system and is appropiate for this question. An answer given in feet or inches would be extremely large in magnitude and difficult for the person asking the question to interpret.

Unlike the English system, however, the metric system units are related in a well-defined and consistent manner. We can convert between metric units by merely moving the decimal point an appropriate number of places. In making a measurement in the metric system we must first recognize the type of measurement and the base unit associated with it. For example, if I wished to report the mass of an object, it would be given relative to the base unit of grams.  The base units for the physical quantities we will commonly be determining are given below in Table 1.
 

Larger and smaller units are constructed by adding prefixes to the appropiate base unit. The prefixes indicate what power of ten the base unit was multiplied by to form the given unit. A complete listing of the metric prefixes are given in Table 2. The prefixes in the white rows are frequently used; you should know their meaning and be able to use them correctly.
 

Table 2. The metric prefixes. The prefixes in the white rows are frequently used and should be memorized.

We often express the meanings of the metric units in normal decimal form with the larger unit being set equal to some multiplier times the smaller unit. For example:

1mL = 1x10^-3L                                                        1cg = 1x10^-2g
Divinding both sides by 1 x10^-3:                                Dividing both sides by 1x10^-2:
1/1x10^-3mL = 1x10³mL = 1000mL                            1/1x10^-2cg = 1x10²cg = 100cg =1g

Because the above relationships are defined, they are exact and have unlimited precision. Therefore, when such relationships are used in dimensional analysis they will not limit the significant figures with which the answer can be reported. You may practice using the defined relationships between metric units as conversion factors, as well as converting from one metric unit to another, in the dimensional analysis tutorial.

Practice Problems:

1. Give the meanings and symbols for the following metric prefixes.
    a) micro
    b) Mega
    c) milli
    d) deci

2. Give the name for each of the following units.
    a) Gm
    b) ns
    c) dL
    d) pg

3. Give the symbol for the following units.
    a) kilogram
    b) centisecond
    c) nanoliter
    d) picometer

4. If you go out to buy a computer today, you will have the opportunity to purchase a hard drive that has the capacity to store a terabyte. How does this compare to a computer hard drive that can store one megabyte?

(answers)

It is important to note that the liter is, by definition, the amount of space occupied by 1 cubic decimeter. 1 L = 1dm³

One decimeter is equivalent to 10 centimeters so the following relationship can be derived between the millillter and the cubic centimeter.

1 dm = 10cm
Cubing both sides of the equation:
1³ dm³ = 10³ cm³
1 dm³ = 1000 cm³= 1L = 1000mL
As a result:
1000cm³ = 1000mL
or
1 cm³ = 1 mL

This relationship between the cubic centimeter and the milliliter is frequently used and should be memorized.
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Answers to Practice Problems:

1.    a) 1x10^-6,m   b) 1x10⁶, M    c) 1x10^-3, m    d) 1x10^-1, d
2.    a) gigameter    b) nanosecond    c) deciliter    d) picogram
3.    a) kg    b) cs    c) nL    d) pm
4.    Since tera- means one trillion and mega means one million, the computer
       with the terabyte hardrive can hold 1,000,000 times more information!

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