Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Irrational number approximation by a rational number

  1. May 20, 2010 #1
    Is there a way ( a theorem ) to find a rational number for a given irrational number such that it is an approximation to it to the required decimal places of accuracy. For example 22/7 is an approximate for pi for 2 decimal places.
     
  2. jcsd
  3. May 20, 2010 #2
    best rational approximation (via continued fractions)
     
  4. May 20, 2010 #3

    mathman

    User Avatar
    Science Advisor
    Gold Member

    There is always the trivial solution. Write out the decimal expansion for the irrational to the required number (plus one) of places. Then truncate (or round). This rational number will satisfy the criterion.
     
  5. May 20, 2010 #4

    lurflurf

    User Avatar
    Homework Helper

    ^That tends to give big denominators, how distasteful.
     
  6. May 21, 2010 #5

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Most of the time you can't do much else.
     
  7. May 21, 2010 #6
  8. Jun 21, 2010 #7
    Write down the decimal expansion to the accurate number of digits required+1 and make the penultimate digit to round figure and then convert it to fraction by dividing it by 10 to power number of decimal digits.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Irrational number approximation by a rational number
  1. Irrational Numbers (Replies: 4)

  2. Irrational numbers (Replies: 9)

  3. Irrational Numbers (Replies: 73)

  4. Rational Numbers (Replies: 2)

Loading...