Question

What $\%$ is $\dfrac{4}{6}$?

Answer 1

Hint: In the question, we have been given a fraction which has to be converted into the percentage form. For this we have to firstly write the decimal form of the given number. So we have to divide the numerator, which is equal to four, by the denominator, which is equal to six. Then finally, on multiplying the decimal form of the given fraction by hundred, we will get the required percentage form of the given number.

Complete step-by-step solution:
The fractional number given to us in the above question is $\dfrac{4}{6}$. Let us consider it as
$\Rightarrow n=\dfrac{4}{6}$
For converting the given fractional number into the percentage form, we first convert the fractional number in the decimal number. For this, we divide the numerator, equal to four, by the denominator, equal to six, as shown below.
\[6\overset{0.66}{\overline{\left){\begin{align}
  & 4 \\
 & \underline{0} \\
 & 40 \\
 & \underline{36} \\
 & 40 \\
 & \underline{36} \\
 & \underline{4} \\
\end{align}}\right.}}\]
From the above division, we can write the decimal form of the given number as \[0.\overline{6}\]. So we can write
$\Rightarrow n=0.\overline{6}$
Now, for converting it into the percentage form, we have to multiply the decimal form of the number by hundred. Therefore, the percentage form of the given number will be
\[\begin{align}
  & \Rightarrow 0.\overline{6}\times 100\% \\
 & \Rightarrow 0.6667\times 100\% \\
 & \Rightarrow 66.67\% \\
\end{align}\]
Hence, the percentage form of the given number $\dfrac{4}{6}$ is $66.67\%$.

Note: While writing the bar representation $0.\bar{6}$ as $0.6667$, we have rounded off the digit at the fourth decimal place. We can also reduce the given fraction to $\dfrac{2}{3}$ by dividing the numerator and the denominator of the given fraction $\dfrac{4}{6}$ by two.