Question

How do you write \[47\% \] as a fraction?

Answer 1

Hint: Here we will use the concept of percentage. We will first convert the given percentage into a fraction and then we will try to simplify the fraction (if there is a common factor between the numerator and denominator) to get the required answer. Percentage and fractions are generally used for comparing different quantities. A fraction is defined as the number of equal parts or in other words parts of a whole quantity.

Complete step by step solution:
Let us understand what the term “percentage” means.
Percentage means part of a whole quantity that is divided into a hundred equal parts.
For example, let us consider a cake.
Let us divide this cake into a hundred equal parts. Now, one slice of the cake means one part of the whole cake. This is a percentage and we can express it as \[1\% \].
The symbol \[\% \] denotes percentages. If we take \[n\] slices of the cake, it means \[n\% \].
We can also express percentages as fractions. Consider the example of the cake. If we take one slice of the cake, it means we are taking one slice out of a hundred slices.
This one portion is \[\dfrac{1}{{100}}\] of the whole cake.
So, a percentage can also be expressed as a fraction, simply by writing the percentage value over 100.
Now, to convert any given percentage into a fraction, say \[n\% \], we will write the value of the percentage i.e., \[n\] with a denominator 100. This means that \[n\% \] is equivalent to \[\dfrac{n}{{100}}\].
We are required to convert \[47\% \] into a fraction. We will write the percentage value i.e., \[47\] with a denominator 100. Therefore,
\[47\% = \dfrac{{47}}{{100}}\]
Since the numerator and denominator do not have any common factor other than 1, it is already in the simplest form.

There \[47\% \] is equal to \[\dfrac{{47}}{{100}}\].

Note:
We know that a percentage can be expressed as decimal as well as fraction. The above method was to convert a whole percentage into a fraction. If we want to convert a percentage that has a decimal value into a fraction, we will write it as a fraction by the above method. Then, we will multiply the numerator and denominator with powers of 10, depending on the number of decimal places. We can also convert any number into a percentage by dividing the number by the whole quantity and then multiplying the result by 100.