Num3er 10/81 Part 1

10
—–   =   0.123456790123456790123456790…
81

Repeating decimal:   0.123456790    (period 9)
 
 
The digit   8   is missing.

The easiest way to remedy this is to subtract   1/10^9,

(10/81) – 1/1000000000 =   9999999919/81000000000   =   0.123456789123456790123456790123456790

Notice that the first   9   is not followed by a   0   or a   10.

We can turn   10/81   into a very cool number:

10/81 – [(3340/3267) * (1/10^9)] = 0.12345678910111213141516171819202122232425262728293031323334353637
38394041424344454647484950515253545556…

 
 
The natural numbers   1, 2, 3, 4, …, 99   appear in this result.
 
 
 

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About benvitalis

math grad - Interest: Number theory
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