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Base three
The base 3 system (also called ternary numeral system) uses the digits 0, 1 and 2.
Explanation
For the numbers between 0 and 1 you can write
03 = 0 0,0013 = 1/27 0,013 = 1/9 0,023 = 2/9 0,13 = 1/3 0,23 = 2/3 0,213 = 7/9 0,223 = 8/9 13 = 1
Conversion to other base
You can convert any base 10 number in a base 3 number. Here are the fractions
1/3 = 2·3-2 + 2·3-3 + 2·3-4 + ... = 0.022222...3 = 0.13 = 0.333...
1/4 = 2·3-2 + 2·3-4 + 2·3-6 + ... = 0.020202...3 = 0.249657054... = 0.25
7/10 = 2·3-1 + 2·3-4 + 2·3-5 + ... = 0.200220022002...3 = 0.674897119... = 0.7
Notations
You can write the number 13 also as 0.222...3 and the number 0.13 also as 0.0222...3 etc. If you see numbers as points on a line segment this may sound quite strange. But mathematics doesn't give a description of reality. Points are no marbles on a cord.