Question

How do you write $\dfrac{14}{35}$ as a decimal?

Answer 1

Hint: In this question, we are given a fraction and we need to change it to decimal. For this we will perform division of 14 by 35 where 14 is the dividend and 35 is the divisor. We will move step by step and step until we get the remainder as 0. As 35 is greater than 14 so we will be using 14.0 as dividend. The quotient obtained will be the required answer.

Complete step-by-step answer:
Here we are given the fraction as $\dfrac{14}{35}$. We need to convert it into decimal. For this let us divide 14 by 35 step by step.
Let us take 14 as dividend and 35 as divisor.
As we can see the dividend is smaller than the divisor so we will take the dividend as 14.0. Our division looks like this, $35\overline{\left){14.0}\right.}$.
We need to solve digits before decimal first. As 14 is smaller than 35 so only possible quotients are 0. So we get remainder as 14.
\[35\overset{0}{\overline{\left){\begin{align}
  & 14.0 \\
 & 0 \\
 & \overline{14} \\
\end{align}}\right.}}\].
As we have reached the decimal point. So we will use it to the quotient and bring one of the zero down. As we know, 35 times 4 is 140 so quotient has 4 as the next digit and remainder becomes zero.
\[35\overset{0.4}{\overline{\left){\begin{align}
  & 14.0 \\
 & 00\downarrow \\
 & \overline{\begin{align}
  & 140 \\
 & 140 \\
 & \overline{00} \\
\end{align}} \\
\end{align}}\right.}}\].
So we can see that with quotient 0.4, 35 fully divides 14.
Hence we can write $\dfrac{14}{35}$ as 0.4
Therefore, the decimal number for $\dfrac{14}{35}$ is 0.4.

Note: Students should note that they can add as many zeroes as they want after the decimal point to get their answers. Take care of when to take the decimal point into the quotient. Note that if after many zeroes are taken we do not get remainder as zero then that decimal could be non-terminating or recurring, so we can take four to five digits after decimal.