# Prove that any number with a recurring decimal expansion is equal to a fraction

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• May 10th 2010, 01:58 PM
Mathman87
Prove that any number with a recurring decimal expansion is equal to a fraction
Can anyone prove that any number with a recurring decimal expansion is equal to a fraction?
• May 10th 2010, 09:05 PM
simplependulum
Try to prove that if it is $0.a_1 a_2 a_3 ... a_n a_1 a_2 a_3 ... a_n a_1 a_2 a_3 ... a_n ...$then it can be writen as a fraction : $\frac{ a_1 a_2 a_3 ... a_n}{999...9}$ or $\frac{ a_1 a_2 a_3 ... a_n}{ 10^n - 1 }$