Question

How do you convert 0.27 (7 repeating) into fraction?

Answer 1

Hint:The question is, we have to convert $0.2777...$ into a fraction. In this, we have to eliminate the number $7777...$ which is present after the decimal point.

For that, we have to consider two equations and by eliminating the number $77777$ 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 take,
$x = $$0.2777...$ … (1)

Multiply with $100$ on both sides,
$100x = 27.777...$ … (2)

Subtract (2)-(1) to eliminate the number $777...$which is present after the decimal point,

$100x = 27.777...$ … (2)
$x = 0.777...$ … (1)

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$99x = 27$
$x = \dfrac{{27}}{{99}}$

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 $0.87$ into a fraction.

For this question, we can directly write $\dfrac{{87}}{{100}}$ as an answer for this problem. Don’t forget that, if we were asked the question in which the last numbers were repeated, we need to solve it by making it as two equations and by eliminating the repeated value, we can get our solution.

Note: In the case of the problem, convert \[0.888...\] to a fraction, we need to approach 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 $\dfrac{8}{9}$.