Repeating Decimals

= 0.010101... (base 2; repeating),

notice that

4 = 1.010101... (base 2; repeating).

Subtracting yields 3 = 1.

This same trick will work with repeating decimals in any base. If, for instance, we instead were handed

= 0.154154154... (base 10; repeating),

then we might consider

1000 = 154.154154... (base 10; repeating).

Subtracting yields 999 = 154.

Return to "Example 2"

Return to "Even More on the Cantor Set"