Question

What is 0.82 as a fraction in simplest form?

Answer 1

Hint: Take the given decimal number as a fraction that is any number can be represented as a fraction by using the denominator as ‘1’. Then multiply the numerator and denominator of the fraction by a certain number such that both numerator and denominator become integers. Then simplify the numerator and denominator with common factors.

Complete step-by-step solution:
Let us assume the given number in decimal form as,
$\Rightarrow x=0.82$
Now, let us represent the above number in fraction using ‘1’ as denominator then we get,
$\Rightarrow x=\dfrac{0.82}{1}$
Here, we can see that if the numerator is multiplied by 100 then the numerator becomes integer.
So, let us multiply the numerator and denominator with 100 then we get,
$\begin{align}
  & \Rightarrow x=\dfrac{0.82\times 100}{1\times 100} \\
 & \Rightarrow x=\dfrac{82}{100} \\
\end{align}$
Here, we can see that both numerator and denominator have a common factor of ‘2’.
Now, by representing the numerator and denominator as the multiples of ‘2’ and removing the common factor then we get,
$\begin{align}
  & \Rightarrow x=\dfrac{2\times 41}{2\times 50} \\
 & \Rightarrow x=\dfrac{41}{50} \\
\end{align}$
Here, we can see that the numerator and denominator of the above fraction do not have any common factors. So, we can conclude that the above fraction is in its simplest form.
Therefore, we can conclude that the fractional representation of given decimal number is, $\therefore 0.82=\dfrac{41}{50}$

Note: The common mistake that can be done is not converting to its simplest form.
Here we got the fractional form of given decimal number as,
$\Rightarrow 0.82=\dfrac{82}{100}$
Here, we cannot give the above fraction as required answer as it is not in simplest form.
Now, we need to convert to simplest form to get the answer as,
$\therefore 0.82=\dfrac{41}{50}$