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Comparing Numbers
Using
Different Methodologies

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Comparing Numbers Computed on a Different Basis -
Comparing "Numbers" without using a Number Line:

Direct Comparison, without using a number line, has many practical advantages because it does not require a physical drawing.

Although a number line provides a visual model which is easy to understand, it is not feasible to use it in most situations. The following limitations make a number line cumbersome and time consuming to use:
  • There is not enough space to physically plot more than a few numbers on the same line graph (number line).


  • Plotting extremely small numbers, or extremely large numbers, or numbers with completely different orders of magnitude, or numbers which are almost equal may each require dramatically different labeling of scale marks. In addition, each situation may require completely different intervals marked on the number line.
Direct Comparison eliminates the problems listed above. Direct comparison does not require a physical drawing.

Real Numbers are sequential. By comparing place values, any two numbers can be compared directly - once the numbers are written in the same standard notation.
Different Methodologies - Comparing numbers computed on a different basis:
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To accurately compare numbers, they must be computed on the same basis, using the same definitions.

If there are differences in methodology, you must recompute the numbers using the same methodology.

Non-comparable information is frequently provided by government. Definitions are changed for various political reasons. Often the methodology used for computation and comparison is obscured. Numbers are computed on different bases from year to year to "spin" the numbers. Comparing non-comparable numbers can be used to show that the economy is growing when it isn't, or certain groups of people need more (or less) government aid, or there aren't enough (or too many) teachers, etc.

However, there is simply no way to compare numbers computed using different definitions as a basis for the calculation. It is absolutely essential to compute numbers on the same basis before comparing them.





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