Question

What is $15.5\% $ as a fraction of lowest terms?

Answer 1

Hint: We have to find the lowest fraction form of $15.5\% $. For that, we will first convert the percentage into fraction according to the steps explained below and then prime factorize the numerator and denominator of the fraction and cancel out the common factors to obtain the lowest fraction form.

Complete step by step solution:
In this question, we are given a number $15.5$ in percentage and we have to convert it in fraction and then bring its simplest form.
First of all, percentage is a ratio of a number expressed as a fraction of 100.
Now, to find the lowest form of $15.5\% $, we will first have to convert this percent into fraction.
Steps to convert percentage into fraction:
Step 1:
Divide the given number by 100.
$ \Rightarrow 15.5\% = \dfrac{{15.5}}{{100}}$
Step 2:
Here, the numerator is in decimal form but we need our answer in pure fraction form. So, for converting the numerator from decimal form to fraction form, multiply both numerator and denominator with 10.
$ \Rightarrow 15.5\% = \dfrac{{15.5}}{{100}} = \dfrac{{15.5}}{{100}} \times \dfrac{{10}}{{10}} = \dfrac{{155}}{{1000}}$
Hence, we have converted $15.5\% $ into pure fraction.
Now, according to our question, we have to find its lowest form. That means we have to cancel all the common factors of both numerator and denominator.
For finding the lowest, first of all prime factorize the given numbers.
$ \Rightarrow \dfrac{{155}}{{1000}} = \dfrac{{5 \times 31}}{{5 \times 2 \times 2 \times 2 \times 5 \times 5}}$
Now, cancel out the common factors.
\[ \Rightarrow \dfrac{{155}}{{1000}} = \dfrac{{31}}{{5 \times 2 \times 2 \times 2 \times 5}} = \dfrac{{31}}{{200}}\]
Hence, $15.5\% $ as the lowest form of fraction is \[\dfrac{{31}}{{200}}\].

Note:
A fraction can be represented in two forms: decimal form and percentage form.
To convert a fraction into decimal, divide the numerator with the denominator.
Example: $\dfrac{{31}}{{200}} = 0.155$
To convert fraction into percentage, multiply the fraction with 100.
Example: $\dfrac{{31}}{{200}} = \dfrac{{31}}{{200}} \times 100 = \dfrac{{31}}{2} = 15.5\% $