Question

What is the decimal of $\dfrac{1}{2}$?

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:
We are asked to find the decimal form of $\dfrac{1}{2}$
Let us assume that the required value as,
$\Rightarrow x=\dfrac{1}{2}$
Here, we can see that the dividend is 1 and the divisor is 2.
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
$\begin{align}
  & 2\overset{0.5}{\overline{\left){10}\right.}} \\
 & \text{ }\underline{-\left( 10 \right)\text{ }} \\
 & \text{ }0 \\
\end{align}$
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
$\Rightarrow x=0.5$
Therefore, the required value in decimal form is given as
$\therefore \dfrac{1}{2}=0.5$

Note: We can solve this question in another method.
We are asked to find the decimal form of $\dfrac{1}{2}$
Let us assume that the required value as,
$\Rightarrow x=\dfrac{1}{2}$
Now, let us convert the denominator as the power of 10 by multiplying some number in both numerator and denominator.
Here, we can see that we get 10 as a denominator when 2 is multiplied by 5.
So, let us multiply by 5 in both numerator and denominator then we get,
$\begin{align}
  & \Rightarrow x=\dfrac{1\times 5}{2\times 5} \\
 & \Rightarrow x=\dfrac{5}{10} \\
\end{align}$
We know that any number can be represented by placing 0 after the decimal point so that the value does not change.
By using this condition in above fraction then we get,
$\Rightarrow x=\dfrac{5.0}{10}$
We know that if the denominator is power of 10 then the decimal form can be obtained directly by moving the decimal point in the numerator to the power of 10 times left side.
Here, we can see that the power of 10 is 1 so that we can move the decimal point 1 time left side in numerator to get the required answer that is,
$\begin{align}
  & \Rightarrow x=0.50 \\
 & \Rightarrow x=0.5 \\
\end{align}$
Therefore, the required value in decimal form is given as
$\therefore \dfrac{1}{2}=0.5$