The periodic fraction into a simple
It is necessary to convert a periodic fraction into a simple one when there is an infinite number, but at the same time it is necessary to obtain its abbreviated form of writing, expressed as an ordinary fraction.
What is a periodic fraction?
The decimal fraction considered here belongs to the infinite class. There is also an infinite non-periodic one: for example, when dealing with numbers like 0.121231234…, 0.787887888… etc.
In general, a periodic fraction is called an infinite decimal, in which, after some sign in the number, the digits begin to repeat, and thus a certain group of them is traced. Actually, these very repeating digits are the so-called significant (or simply periodic) part of the fraction.
When a short record of such a fraction is made, the numbers that are repeated in an infinite number are taken in parentheses. This is called the period of the fraction.