Question

Write down the decimal expansion of the following number: $\dfrac{123}{35}$ .

Answer 1

Hint: To find the decimal expansion of $\dfrac{123}{35}$, divide 123 by 35 and find its quotient up to some decimal places, the quotient will be the decimal expansion of $\dfrac{123}{35}$.

Complete step-by-step answer:
We have to find the decimal expansion of the fraction $\dfrac{123}{35}$. We know that, to find the decimal expansion of a fraction $\dfrac{p}{q}$ , we divide ‘p’ by ‘q’ and the quotient will be the decimal expansion of the fraction $\dfrac{p}{q}$ .
Here, given fraction $=\dfrac{123}{25}$
i.e. $\dfrac{p}{q}=\dfrac{123}{25}$ .
So, here $p=123$ and $q=35$ .
To find the decimal expansion of $\dfrac{123}{35}$, let us divide 123 by 35.
$\begin{align}
  & 35)123(3.51428 \\
 & \text{ }\dfrac{105}{\times \text{180}} \\
 & \text{ }\dfrac{175}{\times 50} \\
 & \text{ }\dfrac{35\text{ }}{150} \\
 & \text{ }\dfrac{140\text{ }}{\times 100} \\
 & \text{ }\dfrac{70\text{ }}{300} \\
 & \text{ }\dfrac{280\text{ }}{\times 200} \\
\end{align}$
As the division is not terminating, we can write the decimal expansion of $\dfrac{123}{35}$ as 3.51428…….

Note: If the division is not terminating, we can write decimal expansion of a fraction up to some decimal expansion by rounding off. We can write $\dfrac{123}{35}=3.51$ (rounding off up to 2 decimal places) or we can write $\dfrac{123}{35}=3.514$(rounding off up to 3 decimal places)