How do you simplify $8 \div \left( {2.4} \right)$?

Hint: First convert $2.4$ into a fraction. For this, write a $1$ as the denominator to make it a fraction and keep the same value. Next, to get rid of the decimal point in the numerator, we count the numbers after the decimal in $2.4$, and multiply the numerator and denominator by $10$ if it is $1$ number, $100$ if it is $2$ numbers, $1000$ if it is $3$ numbers, and so on. Next, divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction. Next, find the reciprocal of $\dfrac{{12}}{5}$ and multiply with $8$. Next, express the product in its lowest terms. We will get the simplified version of $8 \div \left( {2.4} \right)$.

Complete step by step solution:
Given: $8 \div \left( {2.4} \right)$
We have to simplify it.
For this, first we have to convert $2.4$ into a fraction.
So, write a $1$ as the denominator to make it a fraction and keep the same value, like this:
$\dfrac{{2.4}}{1}$
To get rid of the decimal point in the numerator, we count the numbers after the decimal in $2.4$, and multiply the numerator and denominator by $10$ if it is $1$ number, $100$ if it is $2$ numbers, $1000$ if it is $3$ numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by $10$ to get the following fraction:
$\dfrac{{24}}{{10}}$
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of $24$ and $10$ is $2$. When we divide the numerator and denominator by $2$, we get the following:
$\dfrac{{12}}{5}$
Therefore, $2.4$ as a fraction is as follows:
$\dfrac{{12}}{5}$
Now, divide $8$ by $\dfrac{{12}}{5}$.
For this, first find the reciprocal of $\dfrac{{12}}{5}$ and multiply with $8$.
We know that the reciprocal or multiplicative inverse of the rational number $\dfrac{a}{b}$ is $\dfrac{c}{d}$ if $\dfrac{a}{b} \times \dfrac{c}{d} = 1$.
So, the reciprocal of $\dfrac{{12}}{5}$ is $\dfrac{5}{{12}}$.
Now, multiply $8$ with $\dfrac{5}{{12}}$.
$8 \times \dfrac{5}{{12}} = \dfrac{{40}}{{12}}$
Now, express the product in its lowest terms.
So, divide numerator and denominator by $4$.
$8 \times \dfrac{5}{{12}} = \dfrac{{40}}{{12}} = \dfrac{{10}}{3}$
It can also be written as $3.33$ in decimal form.

Therefore, $8 \div \left( {2.4} \right) = \dfrac{{10}}{3}$ or $8 \div \left( {2.4} \right) = 3.33$.

Note: In above question, it should be noted that we multiplied $8$ with the reciprocal of $\dfrac{{12}}{5}$. If we multiply $\dfrac{{12}}{5}$ with the reciprocal of $8$.
Reciprocal of $8$: $\dfrac{1}{8}$.
Now, multiply $\dfrac{1}{8}$ with $\dfrac{{12}}{5}$.
$\dfrac{1}{8} \times \dfrac{{12}}{5} = \dfrac{{12}}{{40}}$
In simplified version, it can be written as
$\dfrac{1}{8} \times \dfrac{{12}}{5} = \dfrac{{12}}{{40}} = \dfrac{3}{{10}}$
So, we get the reciprocal of the actual answer.
Thus, we have to be careful while calculating it.