1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is 2.7177117771117777 irrational?

  1. Oct 14, 2011 #1
    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.
     
  2. jcsd
  3. Oct 14, 2011 #2

    gb7nash

    User Avatar
    Homework Helper

    Re: Is 2.71771177711177771111... irrational?

    Your intuition is correct. The decimal must be repeating the same pattern in order for it to be a rational number. Ergo, this is an irrational number.
     
  4. Oct 14, 2011 #3
    Re: Is 2.71771177711177771111... irrational?

    Thanks! And you didn't recognize it, did you, as a well-known number?
     
  5. Oct 14, 2011 #4

    gb7nash

    User Avatar
    Homework Helper

    Re: Is 2.71771177711177771111... irrational?

    I don't know. I've never seen it.
     
  6. Oct 14, 2011 #5

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Is 2.71771177711177771111... irrational?

    It is somewhat close to e=2.7182818284590....

    ehild
     
  7. Oct 14, 2011 #6
    Re: Is 2.71771177711177771111... irrational?

    Thanks, ehild and gb7nash! I wish I could think of how such a pattern could be generated. WTMTOMH, I guess.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is 2.7177117771117777 irrational?
  1. Irrationality Proofs (Replies: 9)

Loading...