Question

How do you express $\dfrac{3}{8}$ as a percent?

Answer 1

Hint: For converting the given number $\dfrac{3}{8}$ into percentage, we first have to divide the numerator, which is equal to $3$ by the denominator, equal to $8$. On dividing, the fractional form of the given number will get converted into the decimal form. Then the resulting decimal number obtained is to be multiplied with one hundred to get the final percentage form of the given number.

Complete step by step solution:
Let us equate the given number $\dfrac{3}{8}$ to a variable, say $x$, so that we can write the given number in the below equation as
\[\Rightarrow x=\dfrac{3}{8}\]
Now, for converting the above number into percentage, we first have to express it in the decimal form from the given fractional form. For this, we divide the numerator equal to $3$ by the denominator, equal to $8$ as shown below.
$8\overset{0.375}{\overline{\left){\begin{align}
  & 3 \\
 & \underline{0} \\
 & 30 \\
 & \underline{24} \\
 & 60 \\
 & \underline{56} \\
 & 40 \\
 & \underline{40} \\
 & \underline{0} \\
\end{align}}\right.}}$
From the above division, we get $\dfrac{3}{8}=0.375$. Putting this in the above equation, we get
\[\Rightarrow x=0.375\]
Now, the percentage form of the given number is to be multiplied by one hundred to get the required percentage form of the given number. Therefore, multiplying both the sides of the above equation by $100$, we get
\[\begin{align}
  & \Rightarrow 100x=0.375\times 100 \\
 & \Rightarrow 100x=37.5 \\
\end{align}\]
Therefore the percentage form of the given number is $37.5\%$.
Hence, the number $\dfrac{3}{8}$ is expressed as a percentage.

Note: As we know that the order is not important between the multiplication and the division, so we can multiply the given number directly by one hundred. Then on carrying out the required division, we will get the same answer as that obtained in the above solution. But for calculating the percentage, division must be preferred first over the multiplication so as to ease out the calculation. This is due to the fact that multiplying a given number by one hundred is easy as it involves just the shifting of the decimal by two units rightwards.