Question

How do you simplify and make the fraction $\dfrac{18}{25}$ into a decimal?

Answer 1

Hint: To simplify the given fraction, we are going to divide the numerator by denominator. Doing the division will fulfill two tasks, first is the simplification of the fraction and the other task is to get the decimal form of the given fraction.

Complete step by step solution:
The fraction given in the above problem is as follows:
$\dfrac{18}{25}$
Now, we are going to simplify the above fraction by dividing 18 by 25. For that, as you can see that numerator is lesser than the denominator so we have to take the decimal point first and put 0 in front of 18 which we are shown below:
\[25\overset{.}{\overline{\left){180}\right.}}\]
In the above division you can see that we have put decimal in the quotient and also have put 0 in front of 18. Now, we have to find the number which on multiplication to 25 will give a number which is equal to or less than 180. So, if we multiply 7 by 25 then we get 175 which is less than 180.
\[25\overset{.7}{\overline{\left){\begin{align}
  & 180 \\
 & 175 \\
 & \overline{005} \\
\end{align}}\right.}}\]
Now, to solve the above division, we are going to put 0 in front of 5 and then we can easily divide 50.
\[25\overset{.72}{\overline{\left){\begin{align}
  & 180 \\
 & 175 \\
 & \overline{\begin{align}
  & 0050 \\
 & \dfrac{0050}{0000} \\
\end{align}} \\
\end{align}}\right.}}\]
In the above division, as you can see that 50 is easily divided to 25 by 2 times which we have written after .7 of the quotient.
Hence, the decimal form of the given fraction is equal to 0.72.

Note: The alternate way to solve the above fraction is as follows:
$\dfrac{18}{25}$
We know that if we make the denominator of the above fraction as 100 then solving the above fraction is easy so we are going to make the denominator of the above fraction as 100 by multiplying the numerator and the denominator by 4 we get,
$\begin{align}
  & \Rightarrow \dfrac{18\times 4}{25\times 4} \\
 & =\dfrac{72}{100} \\
\end{align}$
Now, the decimal form of the above fraction is found by putting decimal two numbers from the last number. Hence, the answer is:
$=0.72$