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

1. ## 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?

2. 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 $\frac{ a_1 a_2 a_3 ... a_n}{ 10^n - 1 }$