Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I need to prove that any number with a repeating block of digits is a rational number. Someone told me I should first find a method of constructing a rational number in the form a/b from a number with repeating blocks of digits (and to do it with very 'easy' numbers first). I'm still stumped though.

For example, given 0.33333..., how do I show that it equals 1/3?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof: Numbers with repeating blocks of digits are rational

**Physics Forums | Science Articles, Homework Help, Discussion**