Results 1 to 2 of 2

Math Help - last decimal digit

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    13

    last decimal digit

    Calculate the last decimal digit of

    111333 +333111
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2008
    From
    Westwood, Los Angeles, CA
    Posts
    176
    Thanks
    1
    Have you tried exploring much smaller powers of each of those numbers?

    111^1 = 111
    111^2 = 12321
    111^3 = 1367631
    ...
    111^6 = 1870414552161

    Seems relatively safe to say that 111^n (where n is an integer) ends in a 1. Makes sense, considering the ones digit is always going to be a product of previous 1s digits, which are all 1. No matter how many 1s you multiply together, you still end up with a 1s digit of 1.

    Now, 333 is a little trickier, since multiplying a bunch of 3s together gets you a number that ends in:

    3^1 = 3
    3^2 = 9
    3^3 = 27
    3^4 = 81
    3^5 = 243
    3^6 = 729
    3^7 = 2187
    3^8 = 6561

    ...

    Check out the last digits there - they end in 3, 9, 7, 1, 3, 9, 7, 1 - looks like a pattern that repeats after each group of four numbers.

    I'll leave it to you to determine, using the pattern, where 333^111 might fall.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. n repeating digit of decimal number
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: December 22nd 2011, 08:49 AM
  2. Replies: 3
    Last Post: August 20th 2011, 12:09 AM
  3. Leading digit in decimal notation
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: January 17th 2011, 02:50 PM
  4. Binary Digit & Decimal value
    Posted in the Algebra Forum
    Replies: 5
    Last Post: February 22nd 2010, 07:22 PM
  5. decimal digit as final digit
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 25th 2008, 07:18 PM

Search Tags


/mathhelpforum @mathhelpforum