Any rational number can be expressed in decimal base. This expression is, in a colloquial way, what most the people understand by a number with a comma.
Let's explain it with the following example,
$$\dfrac{1}{2}$$ can be written as $$0,5$$.
And then we read zero comma five instead of a half.
This expression is useful if we are referring, for example, to a price or a length, where it is necessary to get the idea of the value of the rational number.
This expression in decimal base is not always exact, for example $$\dfrac{1}{3}=0,33333\ldots$$ and we should write an infinite number of $$3$$, which would take too much time. In this case we will say that the result is a zero comma three repeating.
Whenever we say repeating, we mean that the number must be repeated infinite times.
We write it putting a bar on the repeating number, for example $$\dfrac{1}{3}=0,\widehat{3}$$.
The repeating decimal does not necessatry involve all the numbers behind the comma. The repeating can also be a number of more than one figure. For example $$$\dfrac{1}{55}=0,018181818\ldots=0,0\widehat{18}$$$
In this case the repeating is $$18$$ and the zero does not belong to it. We should read zero comma zero with repeating eighteen.
Given a number with repeating we can recover the expression as quotient using the following procedure.
$$a$$ is corresponding to the number whose comma and repeating numbers we want to remove. $$b$$ is the number to which we have to add the digits of the repeating number $$a$$. Let's say, also, that the decimal part that does not belong to the repeating has $$m$$ numbers and that the repeating itself has $$n$$ numbers. Then, our decimal expression corresponds to the quotient of $$b-a$$ for the number with $$n$$ nines followed by $$m$$ zeros.
It is easier to understand with some examples. Let's see that the expressions of the past examples have a correspondance with a rational number.
For the expression $$0,\widehat{3}$$, according to our notation; $$a=0,b=3,m=0$$ and $$n=1$$. And it corresponds to the quotient
$$$\dfrac{b-a}{9}=\dfrac{3-0}{9}=\dfrac{1}{3}$$$
For the expression $$0,0\widehat{18}$$, according to our notation: $$a=0,b=018,m=1$$ and $$n=2$$. And it corresponds to the quotient
$$$\dfrac{b-a}{990}=\dfrac{18-0}{990}=\dfrac{1}{55}$$$
For the expression $$0,12\widehat{34}$$, according to our notation: $$a=12,b=1234,m=2$$ and $$n=2$$. And it corresponds to the quotient
$$$\dfrac{b-a}{9900}=\dfrac{1234-12}{9900}=\dfrac{611}{4950}$$$
We can verify that the decimal expression corresponds to the original expression.
Now, we can study the rational numbers through their decimal expression. And this decimal expression is a digits sequence. We have studied that rational numbers have a correspondence with the sequences of digits that, at the end, are repeating.