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Math Help - [SOLVED] Problem Solving

  1. #1
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    Exclamation [SOLVED] Problem Solving

    I have solved a problem, but am not so sure if I have the right answer. If anyone can help check it for me and correct what is wrong, if anything, I would greatly appreciate it!


    PROBLEM:
    Jen has to number the 396 pages in her biology notebook. How many digits will she have to write?

    I got the answer 1075 digits by:

    pages 1-9 = 9 digits
    10-99 = 178 digits (99-10 = 89 #s. 89 x 2 digits = 178)
    396-100 = 888 digits (396-100 = 296 #s x 3 digits = 888)

    9
    178
    + 888
    _______
    1075 digits on 396 pages

    Again, if anyone can help go over this it would be a great help!

    Thank you
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  2. #2
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    Correct!

    Good job, you got it right.
    Last edited by Chris L T521; February 2nd 2009 at 02:13 PM. Reason: Removed the poster's request to look at his/her thread.
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  3. #3
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    Great! Thanks!
    Last edited by Chris L T521; February 2nd 2009 at 02:14 PM. Reason: Removed response to request.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by phillyfan09 View Post
    I have solved a problem, but am not so sure if I have the right answer. If anyone can help check it for me and correct what is wrong, if anything, I would greatly appreciate it!


    PROBLEM:
    Jen has to number the 396 pages in her biology notebook. How many digits will she have to write?

    I got the answer 1075 digits by:

    pages 1-9 = 9 digits
    10-99 = 178 digits (99-10 = 89 #s. 89 x 2 digits = 178)
    396-100 = 888 digits (396-100 = 296 #s x 3 digits = 888)

    9
    178
    + 888
    _______
    1075 digits on 396 pages

    Again, if anyone can help go over this it would be a great help!

    Thank you
    actually, there are 90 2-digit #s and 297 3-digit #s (you have to add 1 to include the 10 and the 100 respectively). so the total comes up to 1080
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  5. #5
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    Could you show me how you would work through that?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by phillyfan09 View Post
    Could you show me how you would work through that?
    think of it this way: how many digits are there between 0 and 9 inclusive? 10 right? do we get 10 simply by saying 9 - 0? now, to include the end points when numbering a list, we compute the difference plus 1. so there are 10 digits in a list of integers from 0 to 9 since we have (9 - 0) + 1 = 10

    similarly, going from 10 - 99 for instance, we have (99 - 10) + 1 numbers. the 10 here is like the "0" in my previous example. so you are really counting the numbers as "0, 1, 2, 3, ..." as opposed to "1, 2, 3, ..." that +1 accounts for the "0", that is, the first term in the list.
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  7. #7
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    Thank you!
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