Question

How do you convert $2\dfrac{3}{4}$ into a percent and a decimal?

Answer 1

Hint: In the above problem we have given an improper fraction so first of all we are going to convert this improper fraction into a proper fraction. This conversion will take place by multiplying 4 by 2 and then add this multiplication to 3 and this result of addition is our new numerator and the denominator will remain the same (i.e. 4). Now, to convert the given fraction into percentage, we are going to multiply this fraction by 100. Then to find the decimal of this fraction we are going to divide the numerator by the denominator of this proper fraction.

Complete step by step solution:
The expression given in the above problem is as follows:
$2\dfrac{3}{4}$
Now, the above fraction is an improper fraction so we are going to convert the above fraction into proper fraction as follows:
$\Rightarrow 2+\dfrac{3}{4}$
Taking 4 as L.C.M in the above addition we get,
$\begin{align}
  & =\dfrac{\left( 2\times 4 \right)+3}{4} \\
 & =\dfrac{8+3}{4} \\
 & =\dfrac{11}{4} \\
\end{align}$
So, we have converted the improper fraction into a proper fraction. Now, we are going to find the percentage of this fraction by multiplying 100 to the above fraction then we get,
$=\dfrac{11}{4}\times 100$
In the above fraction, 100 will be cancelled by 4 as 25 times so the above expression will look like:
$\begin{align}
  & =\dfrac{11}{1}\times 25 \\
 & =275 \\
\end{align}$
So, we got the percentage of the above fraction as $275\%$.
Now, to find the decimal of the given fraction $\left( \dfrac{11}{4} \right)$, we are going to divide 11 by 4 and we get,
\[4\overset{2.75}{\overline{\left){\begin{align}
  & 11 \\
 & -8 \\
 & \overline{03}0 \\
 & -28 \\
 & \overline{002}0 \\
 & \dfrac{-20}{0000} \\
\end{align}}\right.}}\]
Hence, the decimal form of the above fraction is 2.75.
Hence, we have calculated the percentage and decimal form of the above fraction.

Note: The other way to find the percentage and decimal of the above improper fraction is as follows:
We can write the above improper fraction as follows:
$\Rightarrow 2+\dfrac{3}{4}$
Now, to find the percentage we are going to multiply the above addition by 100 and then the above fraction will look like:
$\begin{align}
  & =\left( 2+\dfrac{3}{4} \right)\times 100 \\
 & =200+\dfrac{3}{4}\times 100 \\
 & =200+3\times 25 \\
 & =200+75 \\
 & =275\% \\
\end{align}$
And the conversion to decimal of the above fraction is done as follows:
$\begin{align}
  & \Rightarrow 2+\dfrac{3}{4} \\
 & =2+0.75 \\
 & =2.75 \\
\end{align}$