Question

Which number is greater than $\dfrac{1}{2}$?
\[\begin{align}
  & A.0.7 \\
 & B.0.25 \\
 & C.0.48 \\
 & D.0.299 \\
\end{align}\]

Answer 1

Hint: In this question, we need to find the number which is greater than $\dfrac{1}{2}$. For this, we will first change the given function into decimal form using equivalent fractions. After that, we will compare the given decimal with found decimal to check which one of the option is greater than $\dfrac{1}{2}$.

Complete step by step answer:
Here we are given the number as $\dfrac{1}{2}$.
Since all of our options are in decimal, so let us convert this fraction into decimal also.
Denominator of the fraction is 2, but for direct conversion, we need the denominator to be the power of 10 (10,100,1000,.....). Since the nearest power of 10 is 10 itself. So let us change the denominator into 10. For this, let us multiply the numerator and denominator by 5, which will give us an equivalent fraction of $\dfrac{1}{2}$ we get: $\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}$.
Now, we know that, for $\dfrac{x}{10}$ we can write it as 0.x, similarly $\dfrac{5}{10}$ becomes equal to 0.5.
Hence we can say that, $\dfrac{1}{2}=0.5$.
Now let us compare 0.5 with 0.7.
As we know, a greater number at first place to the right of the decimal will give us the whole decimal number as the greater one. So, as 7 is greater than 5 so 0.7 is greater than 0.5.
Comparing 0.25 with 0.5, we see that, 5 is greater than 2, so 0.25 is smaller than 0.5.
Comparing 0.48 with 0.5, we see that 5 is greater than 4, so 0.48 is smaller than 0.5.
Comparing 0.299 with 0.5, we see that 5 is greater than 2, so 0.299 is smaller than 0.5.

Hence we conclude that 0.7 is greater than $\dfrac{1}{2}$.

Note: Students should carefully convert the fraction into decimal. They should note that while comparing, we just need to check the first digit after decimal. Number of digits after decimal does not matter. Make sure to multiply 5 by numerator also, while finding the equivalent fraction.