The short answer to this question is NO.
To represent any number in a given base, means to **measure** it in that base.
1/3 cannot be measured in base 10, so it is foolish to claim that 1/3 = 0.333...
The most important number theorem is described in the following article:
https://drive.google.com/open?id=1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH
https://www.youtube.com/watch?v=yMqGM3B6Zhw
@Henry Hudson GC No, that is not the reason. 1/12 has no measure (repeats) in decimal because its prime factors are 3 and 2x2. However, 3 is not a prime factor of 10.
In order for any number to have a measure in base 10, it must contain no prime factors other than 2 and 5.
For example, 1/3 has no measure in decimal.
https://drive.google.com/open?id=1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH
