Question

How do you convert $0.4\overline{3}$ ($3$ being repeated) to a fraction?

Answer 1

Hint: Fractions represent equal parts of a whole or a collection. Fraction of a whole is given when we divide a whole into equal parts, each part is a fraction of the whole. Fractions also represent parts of a set or collection. We can recognize a fraction by the slash that is written between two numbers. We have an upper number called a numerator and lower number named as denominator.

Complete step-by-step solution:
From the question it had been given that to convert $0.4\overline{3}$ into a fraction.
To convert $0.4\overline{3}$ into fraction we have to do like as shown below,
While converting the recurring decimal we should assume the given decimal as some variable.
Let us first assume $0.4\overline{3}$ be $x$
Since $x$ is recurring in one decimal places, we multiply it by $10$
$x=0.4\overline{3}$
$\Rightarrow 10x=4.33$
Now, let us subtract the both the equations,
By subtracting both the equations we get,
$\Rightarrow 10x-x=4.33-0.43$
$\Rightarrow 9x=3.9$
As a last step, we divide both sides of the equation by $9$ to get $x$ as a fraction.
By dividing the both sides of the equation by $9$ we get,
$\Rightarrow x=\dfrac{3.9}{9}$
$\Rightarrow x=\dfrac{39}{90}$
$\Rightarrow x=\dfrac{13}{30}$
Therefore, $0.4\overline{3}$ can be written in fractional form as $x=\dfrac{13}{30}$.

Note: While answering questions of this type we should be sure with the calculations. To answer this question we need to reduce the given decimal number into a fraction. The process involves assuming the given number as $x$ and multiplying it with $10$. But if we have 2 repeating numbers then we have to multiply with $100$ similarly if $n$ then with ${{10}^{n}}$.