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Thread: base 10?

  1. #1 base 10? 
    Forum Junior DivideByZero's Avatar
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    Don't feel like adding any words...
    just read along and hope to follow it
    if you get confused ignore this post and continue your surfing


    Help meee!!!

    1/9 = .1111...
    .
    .
    9/9 = .9999...

    no numbers between 9 and 10
    usually 9.5 is between 9 and 10

    . (9) (9) (9) (9) (9.5)

    110 = (1) (1) (0)
    1*100, 1*10, 1 = 100+10+0 = 110

    1(1.5)0 = (1) (1.5) (0)
    1*100, 10*1.5, 0*1 = 100+15+0 = 115
    [EDITED]
    (2.1)(10)(3.5) = (2.1)(10)(3.5)
    2.1*100, 10*10, 3.5*1 = 210+100+3.5 = 313.5

    2.1 10 3.5 = 313.5

    im stuck!


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  3. #2  
    Forum Professor sunshinewarrior's Avatar
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    Perhaps you should have hadded words/commentary! :P

    One thing that struck me, in all the blooming, buzzing confusion (cf William James), was this:

    (2.1)(10)(3.5) = (2.1)(10)(3.5)
    2.1*10, 10*10, 3.5*1 = 21+100+3.5 = 124.5


    Why not

    (2.1)(10)(3.5) = (2.1)(10)(3.5)
    2.1*100, 10*10, 3.5*1 = 210+100+3.5 = 313.5 ?


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  4. #3  
    Forum Junior DivideByZero's Avatar
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    Quote Originally Posted by sunshinewarrio
    Perhaps you should have hadded words/commentary! :P

    One thing that struck me, in all the blooming, buzzing confusion (cf William James), was this:

    (2.1)(10)(3.5) = (2.1)(10)(3.5)
    2.1*10, 10*10, 3.5*1 = 21+100+3.5 = 124.5


    Why not

    (2.1)(10)(3.5) = (2.1)(10)(3.5)
    2.1*100, 10*10, 3.5*1 = 210+100+3.5 = 313.5 ?
    yeah thats mighty retarded of me
    but it doesn't change the impact of my post. i'm stuckkkkk!
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  5. #4  
    Forum Professor sunshinewarrior's Avatar
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    The first part of your post, with the tricksy little decimal expansion, seems quite different from the second part that simply explains how Base 10 is to be interpreted. I see no problems with the second part. What problems do you have with it?

    FWIW in the first part, if we are talking about it in Base 10 terms, then we might be able to say something like this:

    0.99999999999....

    = 0*1 + 9*0.1 + 9*0.01 + 9*0.001 ...

    = 9*(0.1 + 0.01 + 0.001 + 0.0001...)

    And then take the limit of the infinite series to show that

    9*(0.1 + 0.01 + 0.001...) = 9*(1)

    = 9

    Thereby returning to your original equation.
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  6. #5  
    Forum Junior DivideByZero's Avatar
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    abc.xyz
    is a number where a is the hundreds place, b is the tens place, c is the onces place, x is the tenths place, y is the hundredths place, and z is the thousandths place.

    i want to write that number without having a separator from whole numbers and fractions. Something like a number system that consists of a whole number base(?) without a separating decimal. sorry if you couldn't follow that.

    I can write 313 and a half by writing 313 then . (dot) then 5 (to represent 5/10 = 1/2 = half)

    but i do not want to use that decimal separator.
    so i rewrote it in (2.1)(10)(3.5) = 2.1 10 3.5 = a number = 313.5

    but i'm stuck here!

    what do i mean by "stuck"?
    I just don't know what to do...

    this is still base 10.
    I don't want a base 10! i was thinking a base infinity but the "tenths place" would never come in handy. unless....
    1 2 =
    1*(infinity) + 2*1 = 2*(infinity)

    8 2 4 =
    8*infinity^2 + 2*infinity + 4*1 = 8x^2 + 2x +4 (treat infinity like a variable)

    but im stuck here again...
    using base infinity to display the number 313.5???
    gahhh


    once again sorry for the lack of commentary. its your choice if you choose to understand this...
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  7. #6  
    Forum Masters Degree bit4bit's Avatar
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    I dont understand exactly what you're trying, but why not do what Sunshinewarrior said, using fractions instead of decimals:

    Quote Originally Posted by sunshinewarrio
    The first part of your post, with the tricksy little decimal expansion, seems quite different from the second part that simply explains how Base 10 is to be interpreted. I see no problems with the second part. What problems do you have with it?

    FWIW in the first part, if we are talking about it in Base 10 terms, then we might be able to say something like this:

    0.99999999999....

    = 0*1 + 9*0.1 + 9*0.01 + 9*0.001 ...

    = 9*(0.1 + 0.01 + 0.001 + 0.0001...)

    And then take the limit of the infinite series to show that

    9*(0.1 + 0.01 + 0.001...) = 9*(1)

    = 9

    Thereby returning to your original equation.
    For example, 1=1/1, 0.1=1/10, 0.01=1/100...etc. That way you dont have to have decimals at all.
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  8. #7  
    Forum Junior DivideByZero's Avatar
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    Quote Originally Posted by bit4bit
    I dont understand exactly what you're trying, but why not do what Sunshinewarrior said, using fractions instead of decimals:

    Quote Originally Posted by sunshinewarrio
    The first part of your post, with the tricksy little decimal expansion, seems quite different from the second part that simply explains how Base 10 is to be interpreted. I see no problems with the second part. What problems do you have with it?

    FWIW in the first part, if we are talking about it in Base 10 terms, then we might be able to say something like this:

    0.99999999999....

    = 0*1 + 9*0.1 + 9*0.01 + 9*0.001 ...

    = 9*(0.1 + 0.01 + 0.001 + 0.0001...)

    And then take the limit of the infinite series to show that

    9*(0.1 + 0.01 + 0.001...) = 9*(1)

    = 9

    Thereby returning to your original equation.
    For example, 1=1/1, 0.1=1/10, 0.01=1/100...etc. That way you dont have to have decimals at all.
    I want to mix fractions in a base 10 structure.
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  9. #8  
    Forum Masters Degree bit4bit's Avatar
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    Do you mean like:

    3135*10<sup>-1</sup> = 313.5
    abcxyz*10<sup>-3</sup> = abc.xyz
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  10. #9  
    Forum Professor serpicojr's Avatar
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    Why do you want to mix fractions and decimals? Doing so introduces a lot of ambiguity into expressions. Decimals expansions are essentially unique, and fractions, although not unique, do always have an obvious choice--r/s, where r and s are integers sharing no common factors and s > 0. A system mixing the two loses this nice property, as far as I can tell. If you were to choose a representative for each number satisfying some nice criteria, you'd probably end up with pure decimals or pure fractions.
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  11. #10  
    Forum Junior DivideByZero's Avatar
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    Quote Originally Posted by bit4bit
    Do you mean like:

    3135*10<sup>-1</sup> = 313.5
    abcxyz*10<sup>-3</sup> = abc.xyz
    no because that is just like abc.xyz in disguise.

    serpicojr, i'm not asking to replace fractions, just thinking of a different way
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  12. #11  
    Forum Masters Degree bit4bit's Avatar
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    Quote Originally Posted by DivideByZero
    no because that is just like abc.xyz in disguise.
    Surely any correct representation of abc.xyz without using decimal places is abc.xyz in disguise?
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  13. #12  
    Forum Junior DivideByZero's Avatar
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    Quote Originally Posted by bit4bit
    Quote Originally Posted by DivideByZero
    no because that is just like abc.xyz in disguise.
    Surely any correct representation of abc.xyz without using decimal places is abc.xyz in disguise?
    in a sense, i guess.
    but i couldn't word it any other way you know..
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