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How do you change \[13\dfrac{1}{3}\% \] to a fraction?

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Last updated date: 13th Jun 2024
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Answer
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Hint: In this question, first we convert a split mixed fraction form of percent into an improper fraction form of a percent. For converting an improper fraction form of percent, first, we write a mixed fraction form of percent into the sum of a whole number and a fraction. Then write the whole number as an equivalent fraction. After that, we added two fractions by using the fraction adding a rule. After that, an improper fraction form of percent comes. Then we convert that into a fraction form. To convert in fraction, we divided the improper fraction form of percent by hundred.

Complete step by step solution:
As we know that the split mixed is the fraction that has a whole number and a fraction. The whole number and a fraction are writing together.
Let’s take an example. a is the whole number and \[\dfrac{b}{c}\] is the fraction number then the split mixed fraction is written as \[a\dfrac{b}{c}\].
Improper: the fraction which has the value in the numerator is greater than the value in the denominator is known as an improper fraction.
Let’s take an example. a is the value of numerator and b is the value of denominator, and a is greater than b. then the improper fraction is written as.
\[\dfrac{a}{b}\;\;\;\;\;\;\left( {where\;a > b} \right)\]
Now come to the question, the split mixed form of percent \[13\dfrac{1}{3}\% \] is given, which is converted into an improper fraction form of a percent.
First, we write the split mixed fraction form of percent into the sum of the whole number and a fraction.
Then, \[13\dfrac{1}{3}\% \] is written as below.
\[ \Rightarrow 13\dfrac{1}{3}\% = \left( {13 + \dfrac{1}{3}} \right)\% \]
Then, we write the whole number in the form of a fraction number as below.
\[ \Rightarrow 13 = \dfrac{{39}}{3}\]
Put that into the above then,
\[ \Rightarrow \left( {\dfrac{{39}}{3} + \dfrac{1}{3}} \right)\% \]
For adding two fractions, we add numerator to numerator. Denominators are common.
Then,
\[ \Rightarrow \left( {\dfrac{{39 + 1}}{3}} \right)\% = \dfrac{{40}}{3}\% \]
Then, the split mixed fraction form of percent \[13\dfrac{1}{3}\% \] is write in the improper fraction form of percent as \[\dfrac{{40}}{3}\% \].
For removing the percentage sign, we divided by the hundred.
Then,
\[ \Rightarrow \dfrac{{40}}{3}\% = \dfrac{{40}}{{3 \times 100}} = \dfrac{{40}}{{300}}\]
We divided both numerator and denominator by twenty.
Then,
\[\therefore \dfrac{{40/20}}{{300/20}} = \dfrac{2}{{15}}\]

Therefore, the fraction of \[13\dfrac{1}{3}\% \] is \[\dfrac{2}{{15}}\].

Note:
If you want to convert a split mixed fraction form of percent into an improper fraction form of a percent. First, you want t0 to convert the whole number into fraction numbers. Then add two fractions. If the denominator is the same for both fractions, then you add both numerators and take the denominator as common.