Question

How do you convert $\dfrac{13}{18}$ to a decimal?

Answer 1

Hint: To convert $\dfrac{13}{18}$ to a decimal, we need to divide the numerator of a fraction by the denominator of a fraction and then see what kind of decimal expression we are getting. In fraction, the numerator is the number which is written above the fraction and denominator is the number which is written below the fraction.

Complete step by step answer:
The number which is given in the above problem of which we have to find the decimal expression is as follows:
$\dfrac{13}{18}$
As you can see that the above number is in the form of a fraction so to find the decimal expression of the above number we have to divide the numerator of the fraction by the denominator. The numerator of the above number is 13 and denominator is 18 so dividing 13 by 18 we get,
$18\overset{0.722}{\overline{\left){\begin{align}
  & 130 \\
 & \dfrac{126}{\begin{align}
  & 040 \\
 & \dfrac{036}{\begin{align}
  & 040 \\
 & \dfrac{036}{040} \\
\end{align}} \\
\end{align}} \\
\end{align}}\right.}}$
In the above division, the 2 written after 7 is of repeating nature. Hence, the decimal representation of $\dfrac{13}{18}$ is as follows:
0.72222222

Hence, from the above, we have converted the given fraction into decimal and the decimal representation is equal to 0.72222222.

Note: You can check whether the decimal representation is correct or not in the following way:
From the above, we got:
$\dfrac{13}{18}=0.72222222$
Now, multiplying 18 on the both sides we get,
$\begin{align}
  & 13=18\times \left( 0.72222222 \right) \\
 & \Rightarrow 13=12.99999996 \\
\end{align}$
Now, if we round off the R.H.S of the above equation we will get 13 which means that L.H.S is equal to R.H.S so the decimal representation that we have written in the solution is correct.
In this way, you can divide 13 by 0.72222222 and see whether the answer is nearly equal to 18 or not.
$\dfrac{13}{0.72222222}=18$