0.2 Repeating as a Simplified Fraction
Introduction
Have you ever wondered how to convert a repeating decimal to a simplified fraction? In this article, we will explore how to convert 0.2 repeating to a simplified fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.2 repeating is a repeating decimal where the sequence "2" repeats indefinitely.
Converting 0.2 Repeating to a Simplified Fraction
To convert 0.2 repeating to a simplified fraction, we can use the following steps:
Step 1: Let x = 0.2 repeating
Let's start by letting x equal to 0.2 repeating.
Step 2: Multiply both sides by 10
Multiply both sides of the equation by 10 to get:
10x = 2.2 repeating
Step 3: Subtract the original equation from the new equation
Subtract the original equation from the new equation to get:
9x = 2
Step 4: Solve for x
Solve for x by dividing both sides of the equation by 9:
x = 2/9
Therefore, 0.2 repeating can be simplified to the fraction 2/9.
Conclusion
In conclusion, we have successfully converted 0.2 repeating to a simplified fraction, which is 2/9. This process can be applied to any repeating decimal to convert it to a simplified fraction.
Practice Exercise
Try converting 0.3 repeating to a simplified fraction using the same steps.
