1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Convert base-10 212 to base-9

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data
    How can you convert 212 in base-10 to base-9?

    3. The attempt at a solution

    There are holes in the sequence of figures when considering 212 in base-9.
    There are 21 holes in the line. There also holes from 90 to 99 and from 190 to 199.
    There are then 40 (= 23+10+10-1) holes in the line, since 198 belongs to the previous sets already.
    This suggests me that the figure in base-9 is at least 242.
    However, the correct answer is 248.
     
    Last edited: Nov 19, 2009
  2. jcsd
  3. Nov 19, 2009 #2

    Mark44

    Staff: Mentor

    21210 = 2*102 + 1*101 + 2*100

    What you want to do is write this number as the sum of multiples of powers of 9, which are 1, 9, 81, 243, and so on.

    How many 81's (= 92) are there? That will be you digit in the 92 place.
    If there's a remainder after subtracting of the 81's, how many 9's are there in that remainder? That will be your digit in the 9's place.
    If there's a remainder (and it better be 5) that will be your 1's place.

    If you're converting 21210 to its base-9 equivalent, 248 IS NOT the correct answer. I don't understand what you're talking about with holes in the line.
     
  4. Nov 20, 2009 #3
    The answer should be [tex](255)_{9}[/tex] . Correct me if i'm wrong.
    212=207+5=23*9+5
    23=2*9+5
    2=0*9+2

    Combining all together,

    212=9(2*9+5)+5=2*9²+5*9+5
    Suggesting 212=[tex](255)_{9}[/tex]
     
    Last edited: Nov 20, 2009
  5. Nov 20, 2009 #4

    ideasrule

    User Avatar
    Homework Helper

    Yes, 255 is right. That's easy enough to check: 2*9^2+5*9+5=212.
     
  6. Nov 20, 2009 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The quick way to do this is: divide 212 by 9. 9 divides into 212 23 times with remainder 5. 9 divides into 23 twice with remainder 5: 21210= 2559.

    That is because saying that 9 divides into 212 23 times with remainder 5 means that 212= 9(23)+ 5. Since 9 divides into 23 twice with remainder 5, 212= 9(9(2)+ 5)+ 5= 2(92)+ 5(9)+ 5.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Convert base-10 212 to base-9
  1. Bases and Vectors (Replies: 4)

  2. Grade 9/10 Algebra. (Replies: 8)

  3. MAA Problem 9/22/10 (Replies: 0)

Loading...