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.

The periodic fraction into a simple
Periodic 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.