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Math Help - Dimensionless Numbers

  1. #1
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    Dimensionless Numbers

    Any dimensionless number multiplied by another dimensionless number is always another dimensionless number right?

    Therefore any scale multiplied by a group of dimensionless numbers is also dimensionless.

    A, B and C are arbitrary scales

    x = (A/B)x' (x' is dimensionless variable),
    y = Cy' (y' is dimensionless variable)

    Then

    xy = (AC/B)x'y' (term is also dimensionless right?)
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  2. #2
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    Quote Originally Posted by davefulton View Post
    Any dimensionless number multiplied by another dimensionless number is always another dimensionless number right?-
    Yes, of course.

    Therefore any scale multiplied by a group of dimensionless numbers is also dimensionless.
    What do you mean by "scale"?

    A, B and C are arbitrary scales

    x = (A/B)x' (x' is dimensionless variable),
    y = Cy' (y' is dimensionless variable)

    Then

    xy = (AC/B)x'y' (term is also dimensionless right?)
    Assuming that A, B, and C are themselves dimensionless, yes.
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