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Before approaching some exercises that can serve as an example of the way in which the Generator Fraction of a pure periodic unlimited Decimal Number must be found, perhaps the most convenient thing is to revise the definition of this operation, in order to understand each one of these procedures within its specific context.
Generatrix fraction of a pure periodic unlimited decimal number
In this sense, we can begin by saying that this operation is a mathematical procedure, whose main objective is to find which is the Fraction from where it comes from, or which is equivalent to a rational number in the form of a decimal expression, whose main characteristic is to count in its incomplete units with a quantity of elements -whether one or a series of them- that are repeated to infinity, immediately after the comma, that separates the integers from the decimals, that is to say, that it is a pure periodic unlimited Decimal Number.
Likewise, Mathematics has pointed out a series of steps that must be followed in order, when finding or finding which is the generatrix Fraction that comes from a decimal number that has these characteristics, and that can be enumerated in the following way:
- When you have a decimal number, whose incomplete units are repeated to infinity, just after the comma, you should begin by summarizing the number, or in other words, express it in a summarized form, placing only the series that makes it up.
- Secondly, when you are right about how many elements make up the period that constitute the incomplete units of the decimal number, start by searching for the Generator Fraction. For this, the complete decimal number will be noted in the space designated for the Numerator: its entire part and its period, without the comma.
- Next, this complete decimal number will be subtracted from the value of the integer that can be found in this number.
- On the other hand, in the Denominator as many nine numbers will be written down as elements have had in their incomplete units the decimal number.
- Once the difference between the decimal number without comma minus the whole part, which will occupy the numerator, and the total number of nines that correspond in the Denominator is obtained, the operation is then given as resolved. That is to say, the Generator Fraction is considered found.
Examples of how to find the Generator Fraction of an unlimited pure newspaper Decimal
Once this definition has been revised, as well as the method suggested by Mathematics, when it comes to solving this operation, it is perhaps much easier to approach each one of the exercises that can serve as an example to the procedure destined to find the Generator Fraction of any pure unlimited periodic decimal number. Here are some of them:
Find the Generatrix Fraction of the following number: 0,888888
At the beginning of the exercise, the incomplete units -or decimal part- of this number should be revised, since they are the ones that will tell with their characteristics what type of decimal it is, and consequently what is the procedure that should be followed to determine its Generator Fraction. Once done, it is observed how incomplete units are made up of a number that extends to infinity, immediately after the comma. Therefore, it is a pure periodic unlimited decimal. Consequently, the first thing to do is to summarize the number:
When this step is fulfilled, it can then be understood that the period of this number is made up of a single element. The Generatrix Fraction must then be constructed. In order to do this, the entire number will be placed in the Numerator, after deleting the comma. The whole part must also be subtracted. However, as in this case, the whole part is made up of zero, this step is eluded. Then simply write down the 8 as numerator, and as denominator a single 9 equivalent to the only element that had the decimal number in its incomplete units:
Find the Generatrix Fraction of the following number: 2,212212212…
Likewise, before this number, in whose incomplete units can be found a series of numbers that repeat to infinity, the first thing that will be done, in order to determine its corresponding generatrix Fraction will be to summarize the number, in order to really see how many elements conform the series that repeats itself in it:
In doing so, it is then concluded that it is a decimal number that in its incomplete units has a period, composed of three elements, which are located immediately after the comma, so it can then be considered as an unlimited decimal number periodic mixed. At the time of constituting its Generatrix Fraction, one will then begin by writing down in the Numerator the complete number, after deleting the comma, minus the numbers that constitute the whole part of this decimal number:
As far as the Denominator is concerned, as many nines will be noted as the element had the period. In this case, three nines will be entered as the denominator:
Find the Generator Fraction of the following number: 456,998799879987
In spite of the extension of this number, as one should always proceed in this type of cases, one should begin by summarizing the number, in order to be able to identify well its parts: the whole and the decimal:
In doing so, it is determined that it is a pure unlimited Decimal Number, whose incomplete units are constituted by four elements, which are repeated to infinity, and are located immediately after the comma is placed. Therefore, at the time of finding its generatrix Fraction, we will begin by writing down in the Numerator the complete number, with the suppressed comma, and subtracting the whole part from this number:
Finally, in the Denominator, the number 9 should be written down four times, for each one of the four elements that make up the period that makes up the decimal part of this number. Once this is done, the operation is considered resolved, that is to say, once the Generatrix Fraction has been found:
October 31, 2019
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