Question

Find the value of $\left[ 3\dfrac{1}{3} \right]\%$ of $90km$

Answer 1

Hint: To find the $\left[ 3\dfrac{1}{3} \right]\%$ of $90km$ , initially we need to solve the value $\left[ 3\dfrac{1}{3} \right]$ and then divide with $100$ to get the fractional value. This fractional value is to be multiplied with $90km$ to get the required answer. The fractional value of $\left[ 3\dfrac{1}{3} \right]$ can be solved using general fraction conversions.

Complete step-by-step solution:
The fraction when evaluated will be $\left[ 3\dfrac{1}{3} \right]=\dfrac{9+1}{3}=\dfrac{10}{3}$
Let the value of required solution be expressed as a variable $x$
From the given question and from basic ideas about percentages, we can write the equation as follows.
$\dfrac{x}{90}\times 100=3\dfrac{1}{3}$
To find the value of $x$ solve the above equation.
Write the fraction $\left[ 3\dfrac{1}{3} \right]$ as $\dfrac{10}{3}$
 $\Rightarrow \dfrac{x}{90}\times 100=\dfrac{10}{3}$
Now divide on the both sides with $100$ , we get
$ \Rightarrow \dfrac{x}{90}\times \dfrac{100}{100}=\dfrac{10}{3}\times \dfrac{1}{100}$
$ \Rightarrow \dfrac{x}{90}=\dfrac{1}{30} $
Multiply on both sides with $90$ , we get
$ \Rightarrow \dfrac{x}{90}\times 90=\dfrac{1}{30}\times 90 $
$ \Rightarrow x=\dfrac{90}{30} $
$ \Rightarrow x=30 $
i.e., $x=30km$ .
Hence as mentioned in the question the value of $\left[ 3\dfrac{1}{3} \right]\%$ of $90km$ is given by $30km$ .

Additional information: Three types of fractions are proper fractions, improper fractions and mixed fractions. The proper fractions are which numerator is less than the denominator. For improper fractions the denominator is less than the numerator. Mixed fraction is a special type of improper fractions which is represented by quotient, remainder. The general form of mixed fractions is $x\dfrac{a}{b}$. Where $x$ is the quotient, $a$ is the remainder and $b$ is the divisor.

Note: The SI unit of length is meters. Which is given by one meter is equal to one thousandth of a kilometer i.e., $1km=1000m$. The fractional value can be represented as percent and vice versa. The percentage of certain distance over the total distance can also be represented in terms of length.