Take the number pi = 3.14159265358979323846264338…. Compute integer multiples of pi . Then truncate the integer so that you only have the decimal part remaining. Graph the decimal part versus its position in the sequence. What do you see? What would be a logical explanation?

multiples of pi |
approximation |
truncation |

pi | 3.141592653 | 0.141592653 |

2*pi | 6.283185306 | 0.283185306 |

3*pi | 9.424777959 | 0.424777959 |

4*pi | 12.56637061 | 0.566370612 |

5*pi | 15.70796327 | 0.707963265 |

Extension:

If you do the same thing with any other decimal number instead of pi, would the observation still be true? Why?