Los Angeles Math Circle

1/24 -- Intermediate: Rational and decimal representations of fractions. (Oleg Gleizer)

We will resume our study of fractions from Problem 8 of the 1/17 handout. We will learn geometric sequences and use them as a tool to find rational representations of real numbers having an infinite recurring part in the decimal form. We will further construct a bijection between the set of rational numbers (p/q, p and q co-prime integers) and the set of real numbers having the terminating (finite) or infinite recurring form.