Convert a decimal number to a fraction

Perhaps best case, before moving forward in an explanation of the correct way in which a decimal number should be converted into a fraction, is to briefly revise some definitions, which will allow us to understand this operation in its precise mathematical context.

Fundamental definitions

In this sense, it may also be prudent to focus this conceptual review on three specific notions: fractions, equivalent fractions, and decimal numbers, which will be of importance as the three types of mathematical expressions related to this conversion operation. Here’s each one:


In this way, it will begin by saying that fractions have been generally explained as a type of mathematical expression, by which you realize fractional numbers, that is, fractions serve to represent amounts that aren´t accurate or not Whole. On the other hand, that discipline also states that fractions shall be composed without exception of two elements, each of which is defined as follows:

  • Numerator: First, you will find the Numerator, which will always be placed at the top of the expression, and that will have the mission to indicate how many parts of the whole have been taken, or represents the fraction.
  • Denominator: On the other hand, the fraction will also have a Denominator, which will be the element at the bottom. Your mission will be to indicate in how many parts the whole is divided, of which the numerator represents some of those parts.

Equivalent fractions

Thus, it will also be relevant to focus attention on the concept of Equivalent Fractions, which will be seen as expressions or fractions, which, despite not having the same amounts, or their numerators or denominators, actually refer to the therefore, the equivalent fractions will be those that indicate the same amount. ´

The most practical way to determine an equivalent fraction will be through cross multiplication, since if fractions actually have an equivalence ratio these multiplications will yield equal results. This operation may be expressed as follows:

Decimal number

Finally, it will also be necessary to throw lights on the concept of the Decimal Number, which will be seen as the numeric expression, composed of an integer and a fractional number, which will be separated by a comma, and used to account for non-number amounts where from a whole, consisting of several units, divided into equal parts, have taken by whole some, and only a few parts of others.

How to pass a decimal number to a fraction

With these definitions in mind, it may certainly be much easier to address an explanation of the steps to be taken when converting a decimal number into a fraction, which will be as follows:

  1. First, the decimal number should be converted into a fraction, which is easily done by placing the unit as a denominator.
  2. It should be found immediately what its equivalent fraction is. For this we will choose a number that can be 10, 100, 1000, etc. and whose number of zeros, when multiplied by the numerator will cause it to become an integer.
  3. Knowing the resulting product will be taken as the new numerator of the equivalent fraction, since when multiplying it by one, it will give the same amount of when the numerator of the first operation is multiplied by the denominator of the second.
  4. If possible, the equivalent fraction could be simplified.
  5. Finally, the obtained fraction is taken as a result of the conversion operation.

Example of how to convert a decimal number to a fraction

However, the best way to complete an explanation of the correct way in which a decimal number should be converted into a fraction may be through the exposure of a particular example, which allows us to see up close how each of the steps are required to resolve an operation like the one shown below:

Convert the next decimal number to a fraction: 0.50


Convert a decimal number to a fraction
Source: Education  
September 30, 2019

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