Question

Which of the following symbols should come in the blank space $0.5\,\_\_\_\_{\left( {0.5} \right)^2}$ ?
A) >
B) =
C) $ \leqslant $
D) <

Answer 1

Hint:
The given expression here is $0.5{\left( {0.5} \right)^2}$. To make the expression true we need to find the relation between the LHS and RHS.
Thus, find the value of ${\left( {0.5} \right)^2}$ and then compare it with LHS.
Hence, find the sign which should be put in the blank space to make the expression true.

Complete step by step solution:
The given expression here is $0.5{\left( {0.5} \right)^2}$.
We need to find the sign to be put in the blank space, which will make the equation true.
To do that, we will solve the LHS and the RHS individually and then compare to get the sign that will make the expression true.
Now, we will solve RHS and compare the values of LHS and RHS.
$\therefore $ Right-hand side
 $ = {\left( {0.5} \right)^2}$
 $ = 0.5 \times 0.5 \\
=0.25 $
Here, we can now observe that by solving LHS and RHS individually, we get LHS > RHS.
So, the sign in the box must be > sign to make the expression true.
$\therefore 0.5\underline {\,\, > \,\,} {\left( {0.5} \right)^2}$

Thus, option (A) is the correct answer.

Note:
To find the greater value from 0.5 and 0.25:
We can write the given decimal values in the rational form of $\dfrac{p}{q}$. Therefore, 0.25 can be written as $\dfrac{{25}}{{100}}$ and 0.5 can be written as $\dfrac{{50}}{{100}}$.
Now, we will compare the numerators of the numbers as their denominators have the same value i.e. 100. So, we can see that, the numerator of $\dfrac{{50}}{{100}}$ is greater than the numerator of $\dfrac{{25}}{{100}}$, i.e. 50 is greater than 25.
So, it is clear that, the value of $\dfrac{{50}}{{100}}$ is greater than the value of $\dfrac{{25}}{{100}}$ .
Hence, we come to a conclusion that 0.5 is greater than 0.25.