Question

Convert $ 0.53 $ ( $ 53 $ repeating) into a fraction.

Answer 1

Hint: The question is, we have to convert $ 0.535353... $ into a fraction. In this, we have to eliminate the number $ 535353... $ which is present after the decimal point. For that, we have to consider two equations and by eliminating the number $ 535353 $ 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 = $ $ 0.535353... $ … (1)
Multiply with $ 100 $ on both sides,
 $ 100x = 53.535353... $ … (2)
Subtract (2)-(1) to eliminate the number $ 535353... $ which is present after the decimal point,
 $ 100x = 53.535353 $ … (2)
        $ x = 0.535353 $ … (1)
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 $ 99x = 53 $
 $ x = \dfrac{{53}}{{99}} $
This is the required solution.
So, the correct answer is “ $ x = \dfrac{{53}}{{99}} $ ”.

Note: In case, if the number after the decimal point doesn’t repeat, there is no need to form two equations. For e.g. Convert 0.56 into a fraction. For this question, we can directly write $ \dfrac{{56}}{{100}} $ as an answer for this problem.
In the case of the problem, convert \[0.7777...\] 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{7}{9} $ .
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.