.9999 Repeating as a Fraction
The decimal .9999 repeating, also known as .9̄, is a fascinating mathematical concept that has sparked debate and discussion among mathematicians and students alike. In this article, we will explore how to convert .9999 repeating to a fraction.
What is .9999 Repeating?
.9999 repeating is a non-terminating, non-repeating decimal that goes on indefinitely in a repeating pattern. It can be written as:
.9̄ = 0.9999...
where the dots indicate that the pattern continues indefinitely.
Converting .9999 Repeating to a Fraction
To convert .9999 repeating to a fraction, we can use a simple algebraic trick. Let's start by letting x = .9999...
Step 1: Multiply Both Sides by 10
Multiply both sides of the equation by 10 to get:
10x = 9.999...
Step 2: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
9x = 9
Step 3: Divide Both Sides by 9
Divide both sides of the equation by 9 to get:
x = 1
The Result
So, .9999 repeating is equal to 1 as a fraction!
What Does This Mean?
This result may seem counterintuitive at first, but it has significant implications in mathematics. It means that the decimal .9999 repeating, which appears to be less than 1, is actually equal to 1. This has far-reaching consequences in calculus, algebra, and other areas of mathematics.
Conclusion
In conclusion, .9999 repeating is equal to 1 as a fraction. This result demonstrates the importance of understanding mathematical concepts and principles, and how they can lead to unexpected and fascinating results.
