Question

How do you convert $0.56$ ($6$ being repeated) to a fraction?

Answer 1

Hint: The question is, we have to convert $0.5666...$ into a fraction. In this, we have to eliminate the number $666...$ which is present after the decimal point. For that, we have to consider two equations and by eliminating the number $666...$ which is present after the decimal point, we are able to convert it into a fraction. Work out more problems in this topic, I have given hints for many similar problems in this solution itself. By doing many problems we are able to attempt this question within 10-15 seconds.

Complete step by step solution:
Let’s consider the given value as \[x\]
$x = $$0.5666...$ … (1)
Multiply with $100$ on both sides,
$100x = 56.666...$ … (2)
Now, we have two equations, since we need a fraction form, we are going to subtract them such that we get some variable in LHS, which can be sent to the denominator such that we attain $\dfrac{p}{q}$, which is a representation of fractional form.
$100x = 56.666...$ … (2)
$x = 0.5666...$ … (1)
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$99x = 56.1$
$x = \dfrac{{56.1}}{{99}}$
This is the required solution.
Hence, we have converted the given number in a fractional representation as required.

Note:
In the case of the problem, to convert \[0.333...\] to a fraction, we need to approach it in the same way by forming two equations. But we have to multiply it with 10 and subtract two equations. Hence, we get the answer as $\dfrac{3}{9}$.

This method is also applicable for the problem, convert $0.55656...$ to fraction. We have to proceed in the same way by multiplying it with 100 and hence two equations were formed. By subtracting both equations we will get the answer. But there is a minute change in this problem, the numerator will be in decimal value. The answer for this problem is $0.55656... = \dfrac{{55.1}}{{99}}$.Solve this problem by yourself and be thorough in this concept.