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

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# Is 2.7177117771117777 irrational?

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