Contents
In this publication, we will consider how a finite or infinite decimal fraction can be converted into an ordinary (simple). We will also analyze the solution of examples for a better understanding of the material presented.
The rule for converting a decimal fraction to an ordinary
To convert a decimal fraction to a simple one, we adhere to the following rules:
1. The integer part of a decimal fraction is the same as the integer part of an ordinary fraction, which in this case will be mixed.
Note: if the integer part of the decimal fraction is equal to zero, then we are dealing with a regular simple fraction (the numerator is less than the denominator).
2. The numbers after the decimal point (fractional part) in a decimal fraction are written in the numerator of the fractional part of an ordinary fraction. At the same time, we discard all zeros.
3. In the denominator of the fractional part of a simple fraction, we write one and the number of zeros equal to the number of digits after the decimal point in the decimal fraction.
Note: Zeros, which can sometimes occur after digits in the fractional part of a decimal, are not counted (according to main property) and can be discarded.
To turn infinite decimal into an ordinary one, it should first be done and only after that the translation should be performed.
To convert infinite periodic decimal fractions to simple fractions, there is a separate one.
Examples
Finite fractions
Example 1
Because there is only one digit after the decimal point, so we write one zero after one in the denominator, and transfer the number 2 to the numerator.
Example 2
Because there are two digits after the decimal point, so we write two zeros after one in the denominator. And in the numerator we transfer only numbers other than zero.
Example 3
Because zeros after the digits in the fractional part of the decimal fraction can be discarded, therefore, only two digits remain, which means only two zeros with a unit in the denominator. The numerator, as in the example above, will contain only one digit 2.
Example 4
We rewrite the integer part of the decimal fraction into the integer part of a simple mixed fraction, and represent the fractional part as a numerator and denominator. The resulting fraction can also be written as an improper fraction.
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Example 5
(mixed fraction)
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(improper fraction)
Example 6
(mixed fraction)
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(improper fraction)
Example 7
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Example 8
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Infinite fractions
Let’s convert the infinite fraction 12,004571231457668723568421… to a common fraction.
Solution
First, let’s round the fraction to 4 digits after the decimal point, i.e. 12,004571231457668723568421… ≈ 12,0046.
Now we can turn this fraction into a simple one.
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