Question

How do you find the fraction notation and simplify $16.6\% $?

Answer 1

Hint: In this type of problem where we need to find the fraction from the percent we must know what percent means. If the person scores $n\% $ it simply means that he scored $n$ out of $100$ and we can write it in the form of the fraction as $\dfrac{n}{{100}}$ and then we can also remove the decimal by multiplying in the denominator of the fraction with $10$.

Complete step by step solution:
Here we are given to find the fraction of term which is given as $16.6\% $
We need to find the fraction from the percent we must know what percent means. If the person scores $n\% $ it simply means that he scored $n$ out of $100$ and we can write it in the form of the fraction as $\dfrac{n}{{100}}$.
So we can write \[16.6\% = \dfrac{{16.6}}{{100}}\]
So we know that whenever we are given the term in the form of decimal we can convert it into the fraction by taking that term in the form of the numerator and denominator. In the denominator comes the ${10^n}$ where $n$ is the number of digits that are present after the decimal in the numerator.
For example: If we have the term $100.12$ so we can write it as $\dfrac{{10012}}{{100}}$
Here we have two terms after the decimal in the numerator, so we have put two zeroes with $1$ in the denominator in order to remove the decimal point from the numerator.
So in a similar way, we know that in $16.6$ we have one digit after the decimal in the given decimal. So we will write ${10^1} = 10$ in the denominator and the decimal will be removed from the numerator.
So we can write:
$16.6 = \dfrac{{166}}{{10}}$
So we can say that:
\[16.6\% = \dfrac{{16.6}}{{100}} = \dfrac{{166}}{{1000}}\]
Now we need to convert it into the simplest form. Here we know that both ${\text{166 and 1000}}$ are divisible by $2$ and hence we can cancel them and we will be getting:
$\dfrac{{166}}{{1000}} = \dfrac{{83}}{{500}}$
Now there is no number that can divide both ${\text{83 and 500}}$ completely.

Hence it is the simplest form of the fraction which is $\dfrac{{83}}{{500}}$.

Note:
Here in this kind of problems, a student can make mistake by leaving the fraction of $16.6$ as $\dfrac{{166}}{{10}}$ which is also one of the answers but to get the proper result we must convert it into the simplest form where both are not divisible by any common factor.