Question

How do I convert a fraction percent like these ones $8\dfrac{1}{2}\% $ and $9\dfrac{3}{4}\% $to decimals?

Answer 1

Hint: As we can see that above question contains fractions and percentage both. To convert them into decimal we will first convert the mixed fraction into improper fractions and then we will break the percentage by dividing with $100$. We can after that convert the fraction into the simplest form by carrying out all the possible factors and then write it into decimal form.

Complete step by step answer:
According to the question we have two mixed fractions. First fraction is $8\dfrac{1}{2}\% $.
We will change this into the improper fraction i.e. $8\dfrac{1}{2}\% = \dfrac{{(8 \times 2) + 1}}{2}\% = \dfrac{{17}}{2}\% $.
Now we will break the percentage by dividing the fraction by hundred: $\dfrac{{17}}{2} \times \dfrac{1}{{100}} = \dfrac{{17}}{{200}}$.
Hence the decimal form of the dfarction $\dfrac{{17}}{{200}}$ is $0.085$.
Now we move to the second fraction which is $9\dfrac{3}{4}\% $. Again we will change this into the improper fraction i.e. $9\dfrac{3}{4}\% = \dfrac{{(9 \times 4) + 3}}{4}\% = \dfrac{{39}}{4}\% $.
Now we will break the percentage by dividing the fraction by hundred: $\dfrac{{39}}{4} \times \dfrac{1}{{100}} = \dfrac{{39}}{{400}}$.
Hence the decimal form of the dfarction $\dfrac{{39}}{{400}}$ is $0.0975$.

Note: We should note that whenever there is a mixed fraction in question, we need to first convert it into improper fractions and then into the simplest form carrying out all the factors from the numerator and denominator. Then we can convert it into percentage or decimal, whatever the question asks. We should know that percentage is a part of the whole. It is a way to represent the selected data in terms of percentage from the whole data.