Math Is Fun Forum

savoy123

Member

Registered: 2008-01-12

Posts: 5

Base 3 to Base 9 - Confusion =(

My apologies for the wrong thread before..

I am extremely confused about this question.
I think my main problem is, I don't understand what the question means. Hopefully someone would be kind enough to briefly show the steps in which I could learn from.

The base three representation of a number x is 12112211122211112222.
Determine the left most digit of the base nine representation of x.

I've been explained with a method with the word "radix" in which I have never heard of. Hopefully you guys don't go too advanced on me!:P

But any help is deeply appreciated.

Thanks.

Last edited by savoy123 (2008-01-20 06:02:04)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Base 3 to Base 9 - Confusion =(

3 times 3 equals 9
so do PAIRS of digits.
12`11`22`11`12`22`11`11`22`22.
5``4``8``4``5``8``4``4``8``8.
III=VIII
00=0 (zero)   0×3 + 0
01=1 (one)    0×3 + 1
02=2 (two)    0×3 + 2
10=3 (three)  1×3 + 0
11=4 (four)    1×3 + 1
12=5 (five)    1×3 + 2
20=6 (six)     2×3 + 0
21=7 (seven)   2×3 + 1
22=8 (eight)    2×2 + 2
100=10 (which means nine)  1×3×3 + 0 + 0
101=11 (which means ten)   1×3×3 +  0 +  1

Last edited by John E. Franklin (2008-01-20 06:43:30)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Base 3 to Base 9 - Confusion =(

Yeah what John said.

This question could have been potentially very difficult, but luckily because 3²=9 we can take a shortcut.

Split your number into pairs (starting from the right) to get:
{12}{11}{22}{11}{12}{22}{11}{11}{22}{22}

You had to start from the right because if the number of digits had been odd then you'd have been left with one digit on its own at the left.

Anyway, to find the leftmost digit of the base 9 number, you just have to convert 12 from base 3 into 9.
John explained how to do that already.

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Why did the vector cross the road?
It wanted to be normal.

savoy123

Member

Registered: 2008-01-12

Posts: 5

Re: Base 3 to Base 9 - Confusion =(

Thank you guys for going into the trouble to explain it to me. It's helped me a lot and I have a clear understanding of it now.
Thanks again!