Examples of how to find the generatrix fraction of a limited decimal

Perhaps the best thing to do, before giving some examples that will allow us to see in practice how any procedure should be performed, aimed at determining how the Generatrix Fraction of a limited decimal number should be found, is to previously review the very definition of this operation, in order to be able to understand each one of these exercises in its proper context.


Generatrix fraction of a limited decimal number

In this sense, we can begin by saying that this operation basically consists of determining which is the fraction that corresponds, or from where it originates, a decimal expression, characterized by being the quotient of an exact division, and having in its incomplete Units a limited number of elements.

With respect to the way in which any procedure must be solved that has as objective then to find the generatrix fraction of a decimal number with these characteristics, Mathematics has indicated a series of steps, that must be followed in the order that is shown next:


  1. Once the decimal number on which the Generatrix Fraction must be found has been offered, it will be necessary to review its elements, especially its incomplete units, since this is what will determine what kind of decimal number it is. If the given number had a precise number of elements in its incomplete units, or decimal part, then it is assumed that it is a limited Decimal.
  2. Once this has been determined, the Generatrix Fraction begins to be constructed, which corresponds to this case. Therefore, the decimal number from which the Generatrix Fraction is being found will be placed in the Numerator. It will be annotated completely, including its entire part, and the comma will be deleted.
  3. In the place of the Denominator, the unit will be annotated, which must be followed by as many zeros as the decimal number has had in its incomplete units, that is to say, in the decimal part, located after the comma.
  4. The generatrix Fraction is considered found. Therefore, the operation can be expressed as solved.

Examples of how to find the Generatrix Fraction of a Limited Decimal Number

Once the concept of this operation has been revised, as well as the steps that must be followed for its solution, it will certainly be much easier to face some exercises that can serve as a practical example of how to apply the method suggested by Mathematics to find the Fraction that generates the limited decimals. Here are some of them:

Example 1

Determine the Generatrix Fraction of the following number: 0.5

To begin with this operation, the decimal part of the number should be checked, finding that it is composed by only one element. Therefore, it is a limited decimal number. Consequently, at the time of finding its Generatrix Fraction, the whole number will be placed in the numerator, suppressing the comma. As the whole part of this number is equal to zero, and when deleting the comma, it becomes a left zero, then only the number 5 is noted in the Numbering:

As for the Denominator, according to the mathematical method for the solution of this operation, the unit must be annotated, followed by as many zeros as decimal elements had the number. In this case, it is a single number, i.e. 5. In this way, 1 followed by zero will be recorded.

The operation is assumed resolved. That is to say, the Generatrix Fraction of the proposed decimal number has been found.

Example 2

Find the Generatrix Fraction of the following number: 2,099

Likewise, the first thing that will be done is to review the amount of elements that the decimal number counts with in its incomplete units or decimal part. In this case there are simply three elements, which leads to the conclusion that it is a limited Decimal Number. In this way, the first thing that will be done, to determine its generating Fraction, will be to place in the numerator all the complete number, without the comma:

On the other hand, in the Denominator a number conformed by the unit should be noted, followed by as many zeros as elements had the decimal part of this number. Therefore, a 1 and three zeros will be recorded, since the decimal part or incomplete units of this number are made up of three elements:

Example 3

Determine which is the Generatrix Fraction of the following number: 1,7777

The exercise also begins by reviewing the elements that have the decimal number in their incomplete units. In doing so, it is found that these are made up of a number that is repeated several times. However, it does so a limited number of times, that is, it does not extend to infinity, so it is not an unlimited periodic decimal number, but a limited Decimal. In this order of ideas, when determining its Generatrix Fraction, this complete number will be noted in the numerator, after suppressing the comma, and in the Denominator, the unit will be noted, followed by as many zeros as there are elements in the decimal part of the number, that is, four zeros (one for each 7):

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Examples of how to find the generatrix fraction of a limited decimal
Source: Education  
October 31, 2019


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