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How did you know that?

To all those experienced students with decimals and fractions, we know that 0.33333... is 1/3 because only the 3 is repeating, so you simply put one 9 in the denominator to get 3/9 or 1/3. Or perhaps... 0.63 repeating can be expressed as 63/99 since two digits are being repeated to get 7/11. (if you didn't know this before hand, it's fine. Now you know :D). A harder question may ask 0.1256, where only 56 part is being repeated. This may be changed to 0.12+56/9900. Yes, there is a pattern, but I want to challenge you to derive this algebraically(use examples if it helps) BONUS: Turn 0.166666.. and 0.2118118118118.... into fractional form

Note by Raymond Park
1 year, 2 months ago

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Thx i learned so much Ian Chiu · 1 year, 1 month ago

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These observations are a result of the following fact:

\[0.\overline{d_1d_2 \cdots d_n}=\frac{d_1d_2 \cdots d_n}{10^n-1} \] where \(d_1, d_2, \cdots, d_n\) denote digits.

The proof is quite simple. Deeparaj Bhat · 1 year, 2 months ago

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