Monday, June 25, 2007

22/7=Pi?

Pi is irrational, or never repeats or ends. Many people believe that 22/7 is pi, but that's just not true. Here are some fractions that are close to pi:(The bolded numbers are the same as pi)
  • 25/8=3.125(exactly)
  • 22/7=3.142857142857142...
  • 223/71=3.140845...
  • 377/120=3.1416666...
  • 3927/1250=3.1416(exactly)
  • 333/106=3.14150943396...
  • 355/113=3.1415929203598...
  • 15707963/5000000=3.1415926(exactly)
  • 103993/33102=3.1415926530119...
  • 104348/33215=3.14159265392142...
  • 10000000000/3183098862=3.141592653429...
  • 208341/66317=3.14159265346743676872...
  • 10471975511/3333333333=3.141592653614...
  • 312689/99532=3.1415926536139...
  • 5419351/1725033=3.14159265358981532046...
  • 837393900/266550757=3.1415926535898001...
  • 80143857/25510582=3.14159265358979267191...
  • 245850922/78256779=3.14159265358979311600...
  • 21053343141/6701487259=3.1415926535897932384623817427748...

You can see that the six digits "142857" repeating in 22/7. If you extend 355/113, you would see 112 digits repeating. Fractions will always repeat, but a number like pi will never repeat.

1 comment:

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