Any real number x can be represented as a continued fraction as:

b
0
x = a + ----------------------
0 b
1
a + ----------------
1 b
2
a + ----------
2
a + ...
3

Typesetters hate this form (quite understandably), and prefer to write continued fractions as:

b b b
0 1 2
a + ---- ---- ---- ....
0 a + a + a +
1 2 3

A simple continued fraction is where all of the b_{n} are all identically equal to 1.

Continued fractions can be used to find best rational estimates for irrational numbers. Functions may also be written as continued fractions, giving successively better rational approximations.