# The Metric Staircase

 | peta +15 The metric staircase below is a graphic way of showing how |__ metric prefixes interact. It is the same thing as the chart |__ above, but in a more visual representation. Each step is | tera +12 a multiple of ten of the lower step. For instance, 'centi' |__ is on the next step above 'milli,' so a centimeter is |__ ten times larger than a millimeter. Centigram is | giga +9 ten times larger than milligram. There are no |__ common metric prefixes for some powers |__ of ten such as +4,+5,-7, etc. | mega +6 |__ |__ | kilo +3 | hecto +2 | deca +1 | ROOT WORD | deci -1 | centi -2 | milli -3 |__ METRIC SYSTEM DEFINITIONS |__ | micro -6 Metric system definitions are relationships |__ between units with the same rootword that, |__ is, only the prefix changes. The Metric Stair- | nano -9 case is just a way to visualize the relationships |__ among the metric prefixes. We make a metric |__ system definition in the following way, using the | pico -12 units kilometer and millimeter as an example: |__ |__ 1.Pick the largest metric prefix. Begin the metric definition with |femto-15 one of the larger units, e.g. 1 km = (some number of) millimeters. | _

2. Count the number of 'steps' down the metric staircase between the two metric prefixes. For instance, kilo- to milli- is six steps.

3. The number of the smaller unit is ten to the power of the number of steps between the metric prefixes. In our example
1 km = E6 mm. Another way to think of it is that the number of zeros of the smaller unit is the number of steps, so
1 km = 1,000,000 mm.

The reason for stating the metric system definitions this way is to make calculations easier and make the sense of the definition more obvious. It is easier to use 1 km = E6 mm than 1 mm = 1/1,000,000 km in math, even though they are both correct.

There are some times you will need to convert between systems. The following few conversion definitions are all you should need to memorize to convert almost anything. Notice we show a "bridge" between the systems in length, volume, and mass to weight.

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