The Power of the Metric System
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What does it mean to have "an entire system based on composing and decomposing units with powers of ten?" The "powers of 10" are 101, 102, 103, 104, and so on. When we compose units with powers of ten we are multiplying by them. When we decompose units with powers of ten we are dividing by them. One thing this means is that any and all conversions between units within the metric system are extremely easy. In a base-10 number system, multiplying or dividing by 10, 100, 1,000, and so on can always be accomplished mentally without complicated computations. The reason for this is that in any base-10 number, each digit tells us how many of a given place value we have. When we multiply by 10 we are simply changing that digit to the next higher place value. When we divide by 10 we are changing that digit to the next lower place value. This coincidence between the base-10 number system and the conversion values within the metric system was, of course, a feature of the metric system's design. If the world had been using a base-20 number system at the time of the French Revolution, the metric system would have been based on powers of 20 rather than powers of 10! The reason the metric system was designed as it was was to facilitate conversions.
Because of the alignment between the metric system and the base-10 number system, we can deepen our understanding of both systems by examining them in an overlapping fashion. One way to do this is to create a typical place value chart and overlay some metric units on that chart.
| 103 (thousands) | 102 (hundreds) | 101 (tens) | 100 (ones) |
| meters | decimeters | centimeters | millimeters |
| liters | deciliters | centiliters | milliliters |
Shown in this manner, the relationships between the metric units are highlighted. The 10-to-1 pattern of our number system is repeated in the 10-to-1 relationship of each of the metric units. In other words, one centimeter is the same as ten millimeters, one decimeter is the same as 100 millimeters, and 1 meter is the same as 1,000 millimeters. While some of the metric units in the chart may be unfamiliar to readers, their existence is important for demonstrating the pattern that is built in to the system.
Elementary Mathematics: Pedagogical Content Knowledge, by James E. Schwartz, is designed to sharpen pre-service and in-service teachers' mathematics pedagogical content knowledge. The five "powerful ideas" (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the text thoroughly integrates discussion of the five NCTM process strands.
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