Is 2.71771177711177771111... irrational? 1. The problem statement, all variables and given/known data I'm student teaching 8th graders Numbers and Operations. This is from an 8th grade activity I inherited with no "answer key." Is this decimal (with a pattern but not a repeating pattern) irrational? I am guessing it is, but I want to confirm it. Also, does anyone know if it is a "famous" number? 2. Relevant equations 3. The attempt at a solution I know that all repeating decimals, such as 2.181818... or 3.156715671567... are rational because they can be represented by fractions a/b, where a and b are integers. And I have studied up on how to convert repeating decimals into fractions. I don't believe this "pattern" in the decimal number in question is "repeating," just a pattern. So I'm thinking it's irrational. But I'm curious about the number itself, also.