SOLUTION: The sequence of numbers 12345678910111213. . . 997998999 is found by writing the numbers 1, 2, 3, . . ., 999 in order. What would be the 1997th digit (from the left) of the lengthy

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The sequence of numbers 12345678910111213. . . 997998999 is found by writing the numbers 1, 2, 3, . . ., 999 in order. What would be the 1997th digit (from the left) of the lengthy      Log On


   

Question 1117174: The sequence of numbers 12345678910111213. . . 997998999 is found by writing the numbers 1, 2, 3, . . ., 999 in order. What would be the 1997th digit (from the left) of the lengthy number?
Answer by ikleyn(52835) About Me  (Show Source):
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1.  First 9 positions are occupied by nine 1-digit numbers from 1 to 9.

    The rest are 1997 - 9 = 1988 positions till the 1997-th position inclusively.



2.  The next 2*90 = 180 positions are occupied by ninety 2-digit numbers from 10 to 99.

    The rest are 1988 - 180 = 1808 positions till the 1997-th position inclusively.



3.  Divide  1808 by 3 to separate 3-digit numbers:  1808%2F3 = 602.667.


    So, there are 602 3-digit numbers starting from 100 till the 1997-th position,

    and the last such number is 100 + 602 - 1 = 701.


    The next 3-digit number 702 has "0" exactly in the 1997-th position.



Answer.  1997-th digit (from the left) of the lengthy number is "0".

Solved.