Question

How do you find the quotient when 4.8 divided by 6.75?

Answer 1

Hint: We start solving the problem by finding the dividend and divisor for the required division process. We then perform the long division by dividing the dividend with the divisor by considering the decimals in the quotient. We continue this division process until we find a repeating sequence in the quotient and then make use of the concept of recurring decimals to find the required value of the quotient.

Complete step by step solution:
According to the problem, we are asked to find the quotient when 4.8 is divided by 6.75.
From the given information, we get the dividend as 4.8 and divisor as 6.75.
We can see that both the divisor and dividend are given in decimals. Now, we need to perform the division process with quotients as a rational number (ie., quotient with decimals is allowed).
Let us perform the division of 4.8 with 6.75 using long division process which is as shown below:
\[\begin{align}
  & \left. 6.75 \right)4.8\left( 0. \right.711 \\
 & \underline{\text{ }0\text{ }} \\
 & \text{ }48 \\
 & \underline{\text{ }47.25\text{ }} \\
 & \text{ }7.5 \\
 & \underline{\text{ }6.75\text{ }} \\
 & \text{ }7.5 \\
 & \underline{\text{ }6.75\text{ }} \\
 & \text{ }0.75 \\
\end{align}\].
We can see that we are getting the same denominator over and over again which means that the next digits will be 1 in the quotient.
We know that this type of decimals are known as recurring decimals and the quotient is denoted as $0.711\overline{1}$.
$\therefore $ So, we have found the quotient when 4.8 divided by 6.75 as $0.711\overline{1}$.

Note: Here we have assumed that the quotient can have decimals otherwise the quotient will be different. Whenever we get this type of problem, we try to find the quotient up to 4-5 places to get the required answer. We should not confuse and make calculation mistakes while performing the division involving the decimals. Similarly, we can expect problems to find the quotient when 5 divided by 7.5.