0.2 Recurring as a Fraction
Introduction
A recurring decimal, also known as a repeating decimal, is a decimal that has a sequence of digits that repeats indefinitely. In this article, we will explore how to convert 0.2 recurring as a fraction.
What is 0.2 Recurring?
0.2 recurring is a decimal that has a sequence of 2s repeating indefinitely. It can be written as:
0.22222... or 0.2̅
This decimal goes on forever, and the sequence of 2s never ends.
Converting 0.2 Recurring to a Fraction
To convert 0.2 recurring to a fraction, we can use the following method:
Let x = 0.22222...
Since the sequence of 2s repeats indefinitely, we can multiply both sides of the equation by 10 to get:
10x = 2.22222...
Now, subtract the original equation from the new equation:
10x - x = 2.22222... - 0.22222...
This simplifies to:
9x = 2
Divide both sides by 9:
x = 2/9
Therefore, 0.2 recurring as a fraction is:
2/9
Conclusion
In this article, we have seen how to convert 0.2 recurring to a fraction. This method can be applied to any recurring decimal to convert it to a fraction. The result is a simple fraction that can be used in various mathematical operations.
