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Math Help - About digits in a number

  1. #1
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    About digits in a number

    Hi,

    Could anyone please tell me if there is any formula or method to find the number of digits in the result of multiplication of 2 numbers?
    For e.g. if a 12 digit number is multiplied by a 16 digit no. then how many digits will be there in the result?

    Thanks.
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  2. #2
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    Opalg's Avatar
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    Quote Originally Posted by san4unall View Post
    Could anyone please tell me if there is any formula or method to find the number of digits in the result of multiplication of 2 numbers?
    For e.g. if a 12 digit number is multiplied by a 16 digit no. then how many digits will be there in the result?
    If a number x has m digits then x must lie between 10^{m-1} and 10^m. If y has n digits then y must lie between 10^{n-1} and 10^n. Then the product xy must lie between 10^{m+n-2} and 10^{m+n}, and therefore has either m+n1 or m+n digits.
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  3. #3
    Member Henderson's Avatar
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    The line between m+n and m+n-1 digits is clear in most cases, depending on the first digits.

    If the first digits are:
    1 and anything 1-4
    2 and 2
    Then there will be m+n-1 digits.

    If the first digits are:
    1 and anything 5-9
    2 and 3
    2 and 4
    3 and 3
    Then it could be either m+n or m+n-1 digits, depending on later digits.

    If the first digits are anything else,
    Then there are m+n digits.
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