Question

The value \[\dfrac{1}{2}\] is what percent of \[\dfrac{1}{3}\]?
a). \[150\]
b). \[200\]
c). \[250\]
d). \[300\]

Answer 1

Hint: Percent is a type of representation of any number out of 100. Percent can be found by the ratio of that number whose percent we have to find and from that number from which we have to find the percent. after multiplying that fraction by 100 we get the value of percent of that number.

Complete step-by-step solution:
Given,
\[\dfrac{1}{2}\] of \[\dfrac{1}{3}\]
To find,
Percent of \[\dfrac{1}{2}\] of \[\dfrac{1}{3}\]
Percent: percent is a type of representation of any number out of \[100\]. We can find the percent of any number. It is not necessary that the percent is always less than \[100\] it may be greater than 100.
We can find the percent by,
\[\text{Percent} = \dfrac{{part\,of\,number}}{{whole(total)\,number}} \times 100\]
\[ \Rightarrow \text{Percent} = \dfrac{{\dfrac{1}{2}}}{{\dfrac{1}{3}}} \times 100\]
\[ \Rightarrow \text{Percent} = \dfrac{1}{2} \div \dfrac{1}{3} \times 100\]
On changing the sign from division to multiplication the expression be like
\[\text{Percent} = \dfrac{1}{2} \times \dfrac{3}{1} \times 100\]
On further calculating:
\[\text{Percent} = \dfrac{3}{2} \times 100\% \]
On dividing further
\[\text{Percent} = 3 \times 50\% \]
\[ \Rightarrow \text{Percent}= 150\% \]
Percent of \[\dfrac{1}{2}\] of \[\dfrac{1}{3}\]is
\[ \Rightarrow\text{Percent} = 150\% \]
Additional information:
Like percent, there are many terms used to represent the small numbers in big fractions. Those terms are like part per million(ppm), in part per million we have to multiply by \[{10^6}\]instead of \[100\]these will increase the fraction of representing. Part per million means one object per 1 million another object. The next term is part per billion(ppb), in part per billion, we have to multiply by \[{10^9}\]instead of 100; this will also increase the fraction of representing the particular number. Part per billion represents one object per 1 billion other objects.

Note: Here is this question we have to use the concept of percent. We find the percent by taking a fraction of two numbers and multiplying that fraction by \[100\] then the obtained fraction is represented in the form of a percent. \[\% \]is the symbol of percent. Percent is not only of \[100\] it can be of any part in the number system. (e.g. \[50\% \]of \[50\] is \[25\]).