Question

What is $33\dfrac{1}{{3 }}\%$ as a fraction and decimal?

Answer 1

Hint: First, we will see what is fraction and decimal
Since the given fractions will be the representation of the number, which are the part of whole numbers.
And the decimal is the alternative way of expressing the fractions after dividing the given terms.
An example for the fraction is $\dfrac{3}{2}$ (rational number) and the decimal for the same value is $1.5$.

Complete step by step answer:
Given that $33\dfrac{1}{{3 }}\%$ is a mixed fraction (not in the conventional form as the values are separated into multiplication and addition).
So first we need to convert the given mixed fraction into the improper fraction, to convert the given mixed fraction as the improper we multiply the given denominator of the proper fraction to get the whole number.
Thus, we get, $33\dfrac{1}{3}\% = \dfrac{{(33 \times 3 + 1)}}{3}$ (attach the number with it and add the numerator)
Further solving this we get, $33\dfrac{1}{{3 }}\% = \dfrac{{(33 \times 3 + 1)}}{{3 }}\% \Rightarrow \dfrac{{100}}{{3 }}\%$
Now the percentage is the representation of numbers and ratio which will be expressed as the fraction of $100$from the given.
Thus, now we are going to convert the given equation into a percentage using the percentage definition,
Hence, we get $33\dfrac{1}{{3 }}\% = \dfrac{{100}}{{3 }}\% \Rightarrow \dfrac{{100}}{3} \times \dfrac{1}{{100}}$
By the use of division operation, we cancel the common terms, thus we get $33\dfrac{1}{{3 }}\% \Rightarrow \dfrac{1}{3}$
Therefore, which is the fraction of $33\dfrac{1}{{3 }}\%$is $\dfrac{1}{3}$
Now using this fraction, we are going to convert them into the decimal that is required.
On dividing the value of $\dfrac{1}{3}$we get, $3\left| \!{\overline {\,
 1 \,}} \right. = 0.3333$ (by the division operation)
Hence, we get the fraction as $\dfrac{1}{3}$and decimal as $0.3333$for $33\dfrac{1}{{3 }}\%$

Note: Important thing while acting the addition or subtraction operation in the fraction is converting the given decimal into the fraction and then solving like if $1.2 + 2.3$ is the question.
Apply the converted part of decimal into a fraction with the base of ten we get, $\dfrac{{12}}{{10}} + \dfrac{{23}}{{10}} = \dfrac{{35}}{{10}}$
Again, converting them into the decimal we get, $\dfrac{{35}}{{10}} = 3.5$hence which is the required answer for $1.2 + 2.3 = 3.5$