Can anyone prove that any number with a recurring decimal expansion is equal to a fraction?

- May 10th 2010, 01:58 PMMathman87Prove 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 PMsimplependulum
Try to prove that if it is $\displaystyle 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 : $\displaystyle \frac{ a_1 a_2 a_3 ... a_n}{999...9} $ or $\displaystyle \frac{ a_1 a_2 a_3 ... a_n}{ 10^n - 1 } $