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Why does 1 over 98 make a pattern of 2 to the N when made into a decimal?
Wiki User
∙ 11y ago
Start with 1/98
Then, since adding and then subtracting 1/100 makes no difference.
= 1/100 + 1/98 - 1/100
= 1/100 + 2/9800
= 1/100 + 2/100*(1/98)
1/98 can thus be expressed in an iterative form where each iteration adds two digits of the pattern (2/100)n.
The iterative formula generates the pattern which persists as long as 2n is less than 100. After that the numbers overlap so that the 1 of the 128 get carried over to the 4 of the 64 so that the number is 0.0102040816326528
Then the 2 (of the next power of 2), 256 get carried over to the 8 to give
0.010204081632653056 so that the pattern is n longer recognisable.
Wiki User
∙ 11y ago
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