Question

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

Answer 1

Hint: To convert $3\dfrac{3}{4}$ into a decimal and percent, we have to convert $3\dfrac{3}{4}$ into a proper fraction. To convert an improper fraction into a proper fraction, we have to multiply the whole number by the denominator and add the numerator to the result. The sum is then divided by the divisor. We will have to perform the division process on this proper fraction, till the remainder becomes 0 and placing a decimal point after the dividend which is followed by zeroes. To convert a number into its percentage, we have to multiply the number by 100.

Complete step by step solution:
We have to convert $3\dfrac{3}{4}$ into a decimal and percent. First, we have to convert $3\dfrac{3}{4}$ into a proper fraction. To convert an improper fraction into a proper fraction, we have to multiply the whole number by the denominator and add the numerator to the result. The sum is then divided by the divisor.
$\Rightarrow \dfrac{\text{Whole number}\times \text{Divisor}+\text{Numerator}}{\text{Denominator}}$
Thus, we can convert $3\dfrac{3}{4}$ into a proper fraction as follows.
Firstly, we have to multiply 3 by 4.
$\Rightarrow 3\times 4=12$
Now, we have to add the numerator to the above result.
$\Rightarrow 12+3=15$
Now, we will divide 15 by the denominator of the given improper fraction.
$\Rightarrow 3\dfrac{3}{4}=\dfrac{15}{4}$
Let us convert $\dfrac{15}{4}$ into decimals. We have to divide 15 by 4. For this, we have to divide till we get the remainder as 0. Firstly, we will write the multiplier which when multiplied by 4 gives the product that is less than or equal to the divisor (15). We know that $4\times 3=12<15$ . Hence, we will write 3 as the quotient and subtract 12 from 15. The result of the subtraction is 3 which is the remainder. Since the remainder is not 0, and there are no digits in the dividend, we have to place a decimal point after 15 which is followed by a 0.
Now the new dividend will be 30. We have to find the multiplier similar to the previous step and continue this process till the remainder is 0.
\[4\overset{3.75}{\overline{\left){\begin{align}
  & 15.00 \\
 & -12 \\
 & \_\_\_\_\_\_ \\
 & \text{ }30 \\
 & \text{ }-28 \\
 & \_\_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & 20 \\
\end{matrix} \\
 & \begin{matrix}
   {} & -20 \\
\end{matrix} \\
 & \_\_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & 0 \\
\end{matrix} \\
\end{align}}\right.}}\]
Hence, the decimal of $3\dfrac{3}{4}$ is 3.75.
Now, we have to convert $3\dfrac{3}{4}$ into a percentage. We know that to convert a number into its percentage, we have to multiply the number by 100. So let us consider the decimal form of $3\dfrac{3}{4}$ , that is, 3.75. Let us multiply this with 100. We know that when a number or decimal is multiplied by 100, we will shift the decimal places two times to the right.
$\Rightarrow 3.75\times 100=375\%$

Hence, the decimal form of $3\dfrac{3}{4}$ is 3.75 and the percentage is 375%.

Note: Students have a chance of making mistakes when converting an improper fraction to a proper fraction. We have considered the decimal form to convert into percentage because it is easy to convert a decimal number to its percentage.