Question

How do you convert $5\dfrac{2}{3}$ into a percent and decimal?

Answer 1

Hint:In mixed fraction we first multiply the denominator to the whole number and then add it to the numerator.
For example,
\[ \Rightarrow 11\dfrac{1}{2} = \dfrac{{(11 \times 2) + 1}}{2} = \dfrac{{22 + 1}}{2} = \dfrac{{23}}{2}\] .
 Again, for finding the percentage we just need to multiply the number by 100.
For example,
$ \Rightarrow \dfrac{{21}}{4} = 5.25$ , therefore, the percentage of 5.25 would be $(5.25 \times 100)\% = 525\% $ .

Complete step by step solution:
The given problem to convert is $5\dfrac{2}{3}$
We first need to change $5\dfrac{2}{3}$ which is the mixed fraction into an improper fraction by multiplying the denominator, that is 3 by the whole number, that is 5 and then we will add the numerator which is 2
By using the above process, we get,
\[ \Rightarrow 5\dfrac{2}{3} = \dfrac{{(3 \times 5) + 2}}{3} = \dfrac{{15 + 2}}{3} = \dfrac{{17}}{3}\]
So, from mixed fraction to improper fraction, we get,
$ \Rightarrow 5\dfrac{2}{3} = \dfrac{{17}}{3}$
Now, we have to divide numerator and denominator to get the decimal
$ = 5.67$.

When 5.67 is converted into a percentage then the two-digit after the decimal shifts to the right side and we get $(5.67 \times 100)\% = 567\% $.

Additional Information:
There are 6 types of fractions; Proper fraction, Improper fraction, Mixed fraction, Like fraction, Unlike fraction and Equivalent fraction. The question which we have solved is an example of a mixed fraction. In a proper fraction, the numerator is smaller and the denominator is larger like $\dfrac{1}{2}$. An improper fraction has a larger numerator and smaller denominator like $\dfrac{3}{2}$. The fractions which have the same denominator is a like fraction. For example, $\dfrac{1}{2},\dfrac{3}{2},\dfrac{5}{2},\dfrac{7}{2}$. $\dfrac{1}{2} + \dfrac{3}{2} + \dfrac{5}{2} + \dfrac{7}{2} = \dfrac{{(1 + 3 + 5 + 7)}}{2} = \dfrac{{16}}{2} = 8$. The fractions which have unequal denominators are called, unlike fractions. For example, $\dfrac{1}{2},\dfrac{1}{3}$. $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{{3 + 2}}{6} = \dfrac{5}{6}$. Whenever the result is the same after simplification, it is known as an equivalent fraction. For example, $\dfrac{1}{2} and \, \dfrac{2}{4}$.

Note: Mixed Fraction is the combination of a whole number and a fraction. And percent simply means a specified amount for every hundred. A decimal number has 2 parts; one is the whole number and the other is the fractional part which is separated by a decimal point.