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anonymous

  • 5 years ago

1. Use the numerals 0, 1, and 2 to write the first 20 numbers in the base 3 numeration system. 2. What is the next number after 222 with a base of 3 ?

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  1. heisenberg
    • 5 years ago
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    it may help to understand what "base 3" means. to help, think of the numbering system you know now. that is called 'base 10' because it goes from 0 to 1 to 2 ... to 9 then back to 0 (10 total numbers). for a base 3 system, you just count 0, 1, 2 then back to 0. it would start like this: 000, 001, 002, 010, 011, 012, 020, 021, 022, 100... in both cases you increment by one and carry over when necessary. make sense?

  2. anonymous
    • 5 years ago
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    I'm sorry I don't. I have a horrible teacher & everything is like another language.

  3. heisenberg
    • 5 years ago
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    so think of a base 10 system (the normal one you're used to). start with 0 and add 1 to the previous number everytime: 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11, 12... you can see that when the rightmost digit "overflows", you add one to the next column over and start back at 0. this is the same principle with base 3 but you only go up to 2 (since there are only 3 digits: 0,1,2). consequently base 3 numbers are: 00, 01, 02, 10, 11, 12, 20, 21, 22, 100...

  4. heisenberg
    • 5 years ago
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    think of each digit acting independent of eachother.

  5. anonymous
    • 5 years ago
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    So next would be 101, 102, 110?

  6. heisenberg
    • 5 years ago
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    that's right!

  7. anonymous
    • 5 years ago
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    then 111 112 120 121 122 130 131?

  8. heisenberg
    • 5 years ago
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    you have to remember: there are no digits above 2 in a base 3 system. so 130 is invalid. the 3 would 'overflow' to 0 and you carry the overflow to the left: 121, 122, 200, 201, 202, 210...

  9. anonymous
    • 5 years ago
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    Ok so what about number 2? How would I find that?

  10. heisenberg
    • 5 years ago
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    so take 222 and add 1, keeping in mind that there are no digits larger than 2.

  11. heisenberg
    • 5 years ago
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    the overflows / "carry-overs" will do so for every digit

  12. anonymous
    • 5 years ago
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    would it be 200

  13. heisenberg
    • 5 years ago
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    not quite. remember, 200 is the same as 0200. base 3 doesn't mean anything about the number of digits in the number, just the types of digits allowed.

  14. anonymous
    • 5 years ago
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    There wouldnt be a number then, right? (Im confused)

  15. heisenberg
    • 5 years ago
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    0222 + 0001 = 1000

  16. heisenberg
    • 5 years ago
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    the same way that 0022 + 0001 = 0100

  17. heisenberg
    • 5 years ago
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    as with any number, you can have as many leading 0's as you want, ie 00002 = 0002 = 2

  18. anonymous
    • 5 years ago
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    okay Thank you so much!!! You are amazing!

  19. heisenberg
    • 5 years ago
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    no problem :)

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