Question

Convert $\dfrac{1}{17}$ to decimal.

Answer 1

Hint: In the above question, we have been given a number in the form of a fraction which we are asked to convert to the decimal. For this, we need to divide the numerator of the fraction, which is equal to one, by the denominator, which is equal to seventeen. On dividing, we will obtain a non terminating infinite decimal expansion for the given fraction. To express the non terminating decimal expansion of the given fraction, we need to use the bar representation and put a bar over the group of the digits which will be repeating infinitely.

Complete step by step answer:
The number given in the above question is equal to $\dfrac{1}{17}$. We can see that it is a fraction. For converting it into the decimal, as is directed in the above question, we have to divide the numerator, which is equal to one, by the denominator, which is equal to seventeen. The division is shown below.
\[17\overset{0.058823}{\overline{\left){\begin{align}
  & 1 \\
 & \underline{0} \\
 & \underline{\begin{align}
  & 10 \\
 & 0 \\
\end{align}} \\
 & \underline{\begin{align}
  & 100 \\
 & 85 \\
\end{align}} \\
 & 150 \\
 & \underline{136} \\
 & 140 \\
 & \underline{136} \\
 & 40 \\
 & \underline{34} \\
 & 60 \\
 & \underline{51} \\
 & 90 \\
\end{align}}\right.}}\]
On continuing the division, we will obtain the decimal expansion of the given fraction as \[0.\overline{0588235294117647}\].

Note: The decimal expansion of the given fraction looks very cumbersome. But then also, if we are asked to write the decimal form of the fraction $\dfrac{1}{17}$, we must write its proper bar representation. We cannot write an approximate decimal expansion for the given fraction, since it will not be exactly equal to the given fraction. Also, since the decimal expansion is quite large, there are many chances of calculation errors while carrying out the division. Therefore we must carry out the division carefully.