Question

How do you write $5.82$ as a fraction?

Answer 1

Hint: Multiply and divide the given number by $100$ as there are two digits after the decimal. The fraction obtained can be reduced, if necessary. Find the greatest common factor of the numerator and the denominator and divide that with the numerator and the denominator to get the simplified form of the fraction.

Complete step by step answer:
We have given $5.82$ which is to be converted to fraction.
For converting to fraction we need to multiply the number by ${{10}^{n}}$ where ‘n’ is the number of digits after the decimal.
Here, the number of digits after decimal is 2 that are ‘8’ and ‘2’
So multiplying and dividing $5.82$ by ${{10}^{2}}=100$, we get
$\begin{align}
  & 5.82\times \dfrac{100}{100} \\
 & \Rightarrow \dfrac{582}{100} \\
\end{align}$
As we know, the common factor between 582 and 100 is 2
So we can conclude that the greatest common factor of 582 and 100 is 2
Dividing the numerator and denominator by ‘2’ we get
$\begin{align}
  & \Rightarrow \dfrac{582\div 2}{100\div 2} \\
 & \Rightarrow \dfrac{291}{50} \\
\end{align}$
This is the simplified form of the fraction and the required solution.

Note: The given number should be rationalised by multiplying ${{10}^{n}}$ where ‘n’ is the number of digits after the decimal. The obtained fraction can be simplified if necessary by dividing the greatest common factor of the numerator and the denominator with both the numerator and the denominator. The final solution should be in maximum simplified form. For example $\dfrac{582}{100}$ is also a fraction, but $\dfrac{291}{50}$ is the appropriate solution to the given question.