Question

How do you convert $5\dfrac{1}{10}$ to a percentage?

Answer 1

Hint: We will first recall the concept of mixed fraction and we will first we will convert the given mixed fraction into improper fraction. We will multiply the obtained fraction with 100 to get the required percentage.

Complete step by step answer:
A mixed fraction is a fraction which consists of a whole number and a fraction part together. Let $a\dfrac{b}{c}$ be a mixed fraction, then ‘a’ will be the whole number and $\dfrac{b}{c}$ will be the fractional part.
We can also write mixed fraction $a\dfrac{b}{c}=a+\dfrac{b}{c}=\dfrac{ac+b}{c}$
So, we can write the mixed fraction $5\dfrac{1}{10}$ as $5+\dfrac{1}{10}$.
We will take $10$ as LCM and then we will multiply 5 with 10 and add the numerator to get the required improper fraction.
$\Rightarrow 5+\dfrac{1}{10}=\dfrac{5\times 10+1}{10}$
$\Rightarrow \dfrac{50+1}{10}$
$\Rightarrow \dfrac{51}{10}$
Now, to convert the obtained fraction into percentage we will multiply it with the 100 and then simplify it to obtain the decimal terms.
$\Rightarrow \dfrac{51}{10}=\dfrac{51}{10}\times 100\%$
$\Rightarrow 51\times 10\%$
$\Rightarrow 510\%$
Hence, we can represent $5\dfrac{1}{10}$ into the percentage as $510\%$.
This is our required solution.

Note: We can also solve the above question alternatively by directly multiplying the $5+\dfrac{1}{10}$ with 100 as $5+\dfrac{1}{10}$ is nothing but expressed from of $\dfrac{51}{10}$.
$\Rightarrow 5+\dfrac{1}{100}=\left( 5+\dfrac{1}{100} \right)\times 100\%$
Now, we will take 100 inside the bracket and multiply it with 5 and $\dfrac{1}{100}$ both.
$\Rightarrow \left( 5\times 100+\dfrac{1}{100}\times 100 \right)\%$
$\Rightarrow \left( 500+1 \right)\%$
$\Rightarrow 501\%$
Also, note that the term percentage (%) means $\dfrac{1}{100}$ so when we have to convert percentage into fraction, we divide the given percentage by 100 and then convert it into proper fraction.