anonymous
  • anonymous
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 ?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
heisenberg
  • heisenberg
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?
anonymous
  • anonymous
I'm sorry I don't. I have a horrible teacher & everything is like another language.
heisenberg
  • heisenberg
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...

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

heisenberg
  • heisenberg
think of each digit acting independent of eachother.
anonymous
  • anonymous
So next would be 101, 102, 110?
heisenberg
  • heisenberg
that's right!
anonymous
  • anonymous
then 111 112 120 121 122 130 131?
heisenberg
  • heisenberg
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...
anonymous
  • anonymous
Ok so what about number 2? How would I find that?
heisenberg
  • heisenberg
so take 222 and add 1, keeping in mind that there are no digits larger than 2.
heisenberg
  • heisenberg
the overflows / "carry-overs" will do so for every digit
anonymous
  • anonymous
would it be 200
heisenberg
  • heisenberg
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.
anonymous
  • anonymous
There wouldnt be a number then, right? (Im confused)
heisenberg
  • heisenberg
0222 + 0001 = 1000
heisenberg
  • heisenberg
the same way that 0022 + 0001 = 0100
heisenberg
  • heisenberg
as with any number, you can have as many leading 0's as you want, ie 00002 = 0002 = 2
anonymous
  • anonymous
okay Thank you so much!!! You are amazing!
heisenberg
  • heisenberg
no problem :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.