Question

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 ?

Answer 1

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?

Answer 2

I'm sorry I don't. I have a horrible teacher & everything is like another language.

Answer 3

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...

Answer 4

think of each digit acting independent of eachother.

Answer 5

So next would be 101, 102, 110?

Answer 6

that's right!

Answer 7

then 111 112 120 121 122 130 131?

Answer 8

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...

Answer 9

Ok so what about number 2?
How would I find that?

Answer 10

so take 222 and add 1, keeping in mind that there are no digits larger than 2.

Answer 11

the overflows / "carry-overs" will do so for every digit

Answer 12

would it be 200

Answer 13

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.

Answer 14

There wouldnt be a number then, right? (Im confused)

Answer 15

0222 + 0001 = 1000

Answer 16

the same way that 0022 + 0001 = 0100

Answer 17

as with any number, you can have as many leading 0's as you want, ie 00002 = 0002 = 2

Answer 18

okay
Thank you so much!!! You are amazing!

Answer 19

no problem :)