Representation
A rational number is represented as a sequence of digits with a quote mark and radix point. For example, 12'3.4 is in quote notation. The radix point may come before the quote mark, as in 12.3'4, or at the same place, as in 12!3 .
The radix point (in base ten it is called a decimal point) has its usual function; moving it left divides by the base; moving it right multiplies by the base. When the radix point is at the right end, the multiplicative factor is 1, and the point can be omitted. Scientific notation may be used as an alternative to the radix point.
We can think of the quote mark as saying that the digits to its left are repeated indefinitely to the left. For example, we can think of 12'34 as the infinite sequence ...1212121234 . If the repeated sequence is 0s, it and the quote mark can be omitted.
The natural numbers look as usual: 0, 1, 2, ..., or, including quote and point, 0!, 0'1., 0'2., ... . The negative integers begin with the digit one less than the base. For example, in decimal, minus three is 9'7 . Numbers beginning with any other repeating sequence are not integers. For example, in decimal, 6'7 is the fraction one-third, and 7'6 is minus one and seven-ninths.
Let and be sequences of digits. Let be the digit one followed by a sequence of zeros of the same length as . Let be the largest digit (one less than the base). Let be a sequence of s of the same length as . Then the number represented by is . For example, 12'345 = 345 − 12000/99 = 7385/33.
Read more about this topic: Quote Notation