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Math Help - Why does the method work? Change a decimal no. from denary(base 10) to octal(base 8)?

  1. #1
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    Why does the method work? Change a decimal no. from denary(base 10) to octal(base 8)?

    K A Stroud Engineering Mathematics 6th ed p.61 frame 133

    Change 0.528_{10} to octal(base 8) form

    Method: every time only multiply the decimal part by 8

    \begin{array}{r}0.526\\\times8\\4.208\\\times8\\1.  664\\\times8\\5.312\\\times8\\2.496\\... goes\ on\end{array}

    answer: 0.4152
    Last edited by BookEnquiry; December 13th 2011 at 04:23 AM.
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  2. #2
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    Re: Why does the method work? Change a decimal no. from denary(base 10) to octal(base

    I couldn't figure it out...

    denary(base 10): 0.526_{10}=5\cdot10^{-1}+2\cdot10^{-2}+6\cdot10^{-3}

    is equal to

    octal(base 8): 0.4152..._{8}=4\cdot8^{-1}+1\cdot8^{-2}+5\cdot8^{-3}+2\cdot8^{-4}+...


    =================================================
    how to get the octal(base 8) answer abcd...?

    denary(base 10): 0.ABC_{10}=A\cdot10^{-1}+B\cdot10^{-2}+C\cdot10^{-3}

    is equal to

    octal(base 8): 0.abcd..._{8}=a\cdot8^{-1}+b\cdot8^{-2}+c\cdot8^{-3}+d\cdot8^{-4}+...
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