Thursday, December 2, 2010

Base inversion and digit ordering

Here's a mathematical curiosity I stumbled onto. The direction in which we write our numbers is just a convention, and as is the numeric base we write them in. But the two are actually closely related. A switch in direction is equivalent to inverting the base.

Consider a number in base 10.

123.410 = 1 × 102 + 2 × 101 + 3 × 100 + 4 × 10-1

In base 1/10, this would be written as

4.3211/10 = 4 × 10-1 + 3 × 100 + 2 × 101 + 1 × 102

Clearly, these are one and the same.




That is all.

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