Since the focus here is on the 10-to-1 relationship, we can choose different units to place in the ones, column, and draw attention to the fact that the 10-to-1 relationship is maintained.
| 103 (thousands) | 102 (hundreds) | 101 (tens) | 100 (ones) |
| kilometers | hectometers | dekameters | meters |
| kiloliters | hectoliters | dekaliters | liters |
| kilograms | hectograms | dekagrams | grams |
In addition to emphasizing the 10-to-1 relationship, we can also use a chart like this to inductively discover the meanings of the metric prefixes. The chart makes clear that deka means ten of the reference units, hecto means 100 of the reference units, and kilo means 1,000 of the reference units. What is less clear, but still accessible through concentrated study of the charts, is that deci means 1⁄10 of, centi means 1⁄100 of, and milli means 1⁄1,000 of.
Again, because of the alignment between the metric system and the base-10 number system, we can obtain increasing levels of precision without having to resort to esoteric fractional numbers. Every step toward greater precision is a step of another power-of-ten partition. Meters can be partitioned into decimeters, decimeters can be partitioned into centimeters, centimeters can be partitioned into millimeters, millimeters can be partitioned into micrometers, and micrometers can be partitioned into nanometers! We need not stop there, because there are additional prefixes available to us. The point is, there is always another level of precision available through another act of partitioning, and that further level of partitioning is always in terms of the 10-to-1 relationship. When we realize that partitioning is a special kind of decomposition, we realize once again the importance of this powerful idea.
Further enhance your math curriculum with more Professional Development Resources for Teaching Measurement, Grades K-5.
