As we've hammered home by now, each physical quantity -- length, mass, volume and so on -- is represented by a specific SI unit. Sometimes, though, the base units have limitations when they're used to measure very small or very large objects. For example, let's say you wanted to measure the length of an ant. Expressed in the SI base unit, an ant's length is 0.003 meters. Now imagine expressing the width of a human hair or an atom in meters: Your numbers would become smaller and smaller -- and increasingly cumbersome. The same holds true for large measurements. The distance between New York City and Los Angeles is 4,493,288 meters, another unwieldy number.

To get around this issue, the General Conference on Weights and Measures adopted a series of prefix names and symbols to designate the decimal multiples and submultiples of SI units. In 1960, enough prefixes existed to cover multiples ranging from 10^{12} to 10^{-12}. But over the years, new prefixes entered the system to accommodate ever larger and smaller values. The accompanying table lists some of the approved prefix names and symbols.

Now we can go back to our examples to see the advantage of using a prefix system based on powers of 10. An ant's length may be 0.003 meters, but it's much more practical to describe something that small in millimeters. To convert meters to millimeters, you simply multiply the length by 1,000, or move the decimal point to the right three spaces. That tells us that an ant is 3 millimeters (3 mm) from its head to its abdomen. And what about our trip between New York City and Los Angeles? You'd be much better off measuring such a great distance in kilometers. To convert meters to kilometers, you simply divide the distance by 1,000, or move the decimal to the left three spaces. That makes your final distance 4,493 kilometers (4,493 km).

All of the prefixes operate in a similar way. The one curveball you need to worry about is the kilogram, the only SI base unit whose name and symbol include a prefix. You might be tempted to add a prefix to kilogram (microkilogram, for example), but that would be incorrect. Instead, you should attach prefix names to the unit name "gram" to represent larger and smaller values of an object's mass. So, for example, 10^{-6} kilograms would be equal to 1 milligram (1 mg).

Armed with the SI units and prefixes, you have everything you need to start measuring metric. In fact, most of the world has been doing so for decades. Up next, we'll discover why nations have enthusiastically embraced the modern metric system and what can happen when a country (yeah, we're looking at you, America) fails to make the switch.

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