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I'm not sure if there is a simple way to obtain 0.99999999(9). \(\frac{9}{9}\) should result in 0.9999(9), but \(\frac{9}{9}\) = 1. Can any gurus answer this?

I'm not sure if there is a simple way to obtain 0.99999999(9). \(\frac{9}{9}\) should result in 0.9999(9), but \(\frac{9}{9}\) = 1. Can any gurus answer this?

another easy way to solve this problem and problems of this nature

0.36363636....

so the 36 part is repeating after the decimal

suppose x = 0.36363636 .... so 100X = 36. 36363636 .... now why did I take 100 ? because I wanted to get a string of the repeating part before the decimal

We are dealing with a repeating decimal in this question. It's helpful to know that there's a way to write these kinds of decimals as a fraction. For example, the repeating decimal 0.444444444(4) may be written as \(\frac{4}{9}\). So, \(\frac{5}{9}\), \(\frac{7}{9}\) and \(\frac{8}{9}\) will all be repeating decimals. You might check it in your calculator. In order to make two decimal points repeat, you have to divide the two digit number by 99. For example, \(\frac{23}{99} = 0.232323232323(23)\). Similarly, \(\frac{36}{99} = \frac{4}{11} = 0.36363636(36)\). Now it's clear that the minimum value of \(m = 4\).

can i sum up lke this? when singularly repeated(.44444..) some number is divided by 9, if two digit repeated(.363636...) then by 99? same goes for 11 then? got the answer correct by picking up but couldnt get your method