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Math Help - explain decimal system urgently

  1. #1
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    explain decimal system urgently

    hello friends,

    My teacher said, in decimal system, Each digit appearing to the left of the decimal point represents a value between zero and nine times an increasing power of ten. Digits appearing to the right of the decimal point represent a value between zero and nine times an increasing negative power of ten.

    Could anyone explain to me this paragraph?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by learning_maths View Post
    hello friends,

    My teacher said, in decimal system, Each digit appearing to the left of the decimal point represents a value between zero and nine times an increasing power of ten. Digits appearing to the right of the decimal point represent a value between zero and nine times an increasing negative power of ten.

    Could anyone explain to me this paragraph?
    take 123.456

    the 1 is in the hundreds position, so it is expressed as 1 x 10^2

    for the 2, it is 2 x 10^1

    the 3, it is 3 x 10^0

    the 4, it is 4 x 10^{-1}

    the 5 is 5 x 10^{-2}

    the 6 is 6 x 10^{-3}

    that's all you teacher was saying and obviously this is true. if you sum all the things i gave you together you get 123.456
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  3. #3
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    What this means is that I can write a number as the sum of powers of ten times positive integer numbers less than 10. Perhaps the best way to understand this is to do some examples.

    example 1:
    4329 = 4000 + 300 + 20 + 9 = 4(10^3) + 3(10^2) + 2(10^1) + 9(10^0)

    The whole number 4329 is really the sum of integers less than 10 times powers of ten.

    example 2:
    16.432 = 10 + 6 + .4 + .03 + .002 = 1(10^1) + 6(10^0) + 4(10^{-1}) + 3(10^{-2}) + 2(10^{-3})

    This is what is called writing in the base 10 numbering system.
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  4. #4
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    Thank you friends.
    Very nice explanation.
    Now I got it. Really it is amazing forum. I think now I can get full marks in Maths.

    Although I understand what exactly my teacher wanted to say, I have one more doubt friend.

    what exactly (between zero and nine times an increasing power of ten) means?????

    actually what the word "times" means here? Is it multiply?
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