Question

What is $\dfrac{9}{2}$ in the decimal?

Answer 1

Hint: Divide the numerator with the denominator using the simple division. If the remainder is less than the divisor then use the decimal point in the quotient and give 10 times the remainder. Then the remainder will be greater than the divisor so that the division continues until we get ‘0’ as the remainder.

Complete step-by-step solution:
Let us assume that the required value as,
$\Rightarrow x=\dfrac{9}{2}$
Here, we can see that the dividend is 9 and the divisor is 2.
Now, let us use the normal division for the above division then we get,
$\begin{align}
  & 2\overset{4}{\overline{\left){9}\right.}} \\
 & \text{ }\underline{-\left( 8 \right)} \\
 & \text{ }1 \\
\end{align}$
Here, we can see that the remainder is ‘1’.
We know that the number ‘1’ is less than ‘2’ which is the divisor.
Now, let us use the decimal point in the quotient and take the remainder to its 10 times then we get
$\begin{align}
  & 2\overset{4.5}{\overline{\left){9}\right.}} \\
 & \text{ }\underline{-\left( 8 \right)\text{ }} \\
 & \text{ }10 \\
 & \text{ }\underline{-\left( 10 \right)} \\
 & \text{ }0 \\
\end{align}$
Here, we can see that the remainder is ‘0’ which suggests that the division is completed.
So, we can say that the required value in decimal as
$\Rightarrow x=4.5$
Therefore, the required value in decimal form is given as
$\therefore \dfrac{9}{2}=4.5$

Note:The common mistake one can do is if there is a remainder less than divisor even after taking one decimal point. Suppose if the fraction is given as $\dfrac{9}{4}$ then the division up to one decimal form is given as
$\begin{align}
  & 4\overset{2.2}{\overline{\left){9}\right.}} \\
 & \text{ }\underline{-\left( 8 \right)} \\
 & \text{ }10 \\
 & \text{ }\underline{-\left( 8 \right)} \\
 & \text{ }2 \\
\end{align}$
Here, we can see that after decimal the remainder is less than divisor.
Now there will be no need to give other decimal point in quotient because a number have only one decimal point and can continue the same process then we get,
$\begin{align}
  & 4\overset{2.25}{\overline{\left){9}\right.}} \\
 & \text{ }\underline{-\left( 8 \right)} \\
 & \text{ }10 \\
 & \text{ }\underline{-\left( 8 \right)} \\
 & \text{ }20 \\
 & \text{ }\underline{-\left( 20 \right)} \\
 & \text{ }0 \\
\end{align}$
So, the required answer is
$\therefore \dfrac{9}{4}=2.25$