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 Subject: "The number 0.142857....." Previous Topic | Next Topic
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Zakatos
Member since Sep-16-03
Dec-02-03, 00:22 AM (EST)     "The number 0.142857....."

 Hello again, thanks everyone for the precious info about my study concerning FPD's (Fully Periodic Decimals, as myself named such elements), I was having trouble to find some time to spend studying more about the subject, but I'll carefully analyze the topic all you pointed me out soon enough.Meanwhile I noticed something somewhat related to the example I gave you of one of FPD's (the "first" FPD speaking ordinally), 1/7 aka 0,142857.... Notice that this number can be written as the sequence:7^-2 * 2^1 = 0,14+7^-4 * 2^2 = 0,0028+7^-6 * 2^3 = 0,000056+7^-8 * 2^4 = 0,00000112+7^-10 * 2^5 = 0,0000000224+...= 0,142857142857142857...Any comments? :)

Zakatos
Member since Sep-16-03
Dec-02-03, 01:26 AM (EST)     1. "RE: The number 0.142857....."
In response to message #0

 Sorry I wrote something wrong. Here it goes:1 / 7 = (7 * 10^-2 * 2) + (7 * 10^-4 * 4) + (7 * 10^-6 * 8) + ... = (7*2^1 / 10^2) + (7*2^2 / 10^4) + (7*2^3 / 10^6) + ... =SUM ( k = 1 to +oo ) OF ( 7*2^k / 10^2k )

Member since Aug-14-05
Nov-05-05, 10:54 AM (EST)    2. "RE: The number 0.142857....."
In response to message #0

 This is great! is this the unique fraction that can be calculated this way, or are there any others?

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