# Continued Fractional representation of irrational numbers [duplicate]

I know that any rational number can be expressed as a continued fraction, but what about irrational numbers? For example, what is the continued fractional representation of Pi, or e for that matter? Can all real numbers be expressed as continued fractions? For example, can the following number be expressed as a continued fraction?

0.1234567891011121314...

• From the second paragraph of the Wikipedia article on continued fractions: "every irrational number $\alpha$ is the value of a unique infinite continued fraction..." (which, combined with the fact that every rational number can be expressed as a continued fraction, means that all real numbers can). Commented Jun 24, 2013 at 4:04
• In fact, $\pi$ has a very nice continued fraction decomposition. Commented Jun 24, 2013 at 4:06
• Every real number has a representation as a simple continued fraction. For irrationals the expression is unique. Commented Jun 24, 2013 at 4:15