Question

How do you convert $0.325$ ($25$ repeated to a fraction)?

Answer 1

Hint: The question is, we have to convert $0.3252525...$ into a fraction. In this, we have to eliminate the number $252525...$ which is present after the decimal point. For that, we have to consider two equations and by eliminating the number $252525$ 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 answer:
Let’s take,
$x = $$0.3252525...$ … (1)
Multiply with $100$ on both sides,
$100x = 32.525252...$ … (2)
Subtract (2)-(1) to eliminate the number $252525...$which is present after the decimal point,

$100x = 32.525252...$ … (2)
$x = 0.3252525...$ … (1)
$ \overline{99x = 32.2 \;\;\;\;\;\;\;\;}$

$x = \dfrac{{32.2}}{{99}}$
This is the required solution.

Additional information: In case, if the number after the decimal point doesn’t repeat, there is no need to form two equations. For e.g. Convert 0.95 into a fraction. For this question, we can directly write $\dfrac{{95}}{{100}}$ as an answer for this problem.

Note: 1. In the case of the problem, to convert \[0.8888...\] 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 $\dfrac{8}{9}$.
2. This method is also applicable for the problem, convert $0.51717...$ 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 $0.51717... = \dfrac{{51.2}}{{99}}$. Solve this problem by yourself and be thorough in this concept.