Question

How do you write $8.4$ as a fraction?

Answer 1

Hint:
In this problem we need to convert the given decimal value into fraction. For this we need to observe the decimal value and note down the number of digits there after the decimal point. We will consider the given value as $x$ and consider it as equation one. Now we will multiply and divide the given value with ${{10}^{n}}$ where $n$ is the number of digits after the decimal point. Now simplifying the obtained equation will give the fraction form of the given decimal value. If there are any common factors for the numerator and denominator then cancel them and simplify the fraction.

Complete step by step solution:
Given that, $8.4$.
In the above number there is one digit after the decimal part which is $4$.
Let us assume that $x=8.4....\left( \text{i} \right)$
We have one digit after the decimal hence the value of $n$ is $n=1$.
$\therefore $ Multiplying and dividing the given value in the equation $\left( \text{i} \right)$ with ${{10}^{n}}={{10}^{1}}=10$ , then we will get
$x=8.4\times \dfrac{10}{10}$
Simplifying the above equation, then we will get
 $x=\dfrac{84}{10}$
We have the number $84$ in the numerator and the number $10$ in the denominator. We can observe that the both numbers are divisible by $2$. So, we can write the above equation as
$x=\dfrac{2\times 42}{2\times 5}$
Cancelling the common terms in the both numerator and denominator, then we will get
$x=\dfrac{42}{5}$

So, the fraction form of the decimal value $8.4$ is $\dfrac{42}{5}$.

Note:
In the question they have not mentioned that the digits after the decimal point are not repeated. If they have mentioned that the digits after the decimal point are repeated then we need to follow the different method to convert the given value into fraction.