.9999 as a Fraction
The decimal .9999 is a non-terminating, non-repeating decimal that has been a subject of interest among mathematicians for a long time. In this article, we will explore how to convert .9999 into a fraction.
What is .9999?
.9999 is a decimal that has an infinite number of 9's. It is a non-terminating decimal, meaning that it cannot be expressed exactly as a finite decimal. It is also a non-repeating decimal, meaning that the sequence of digits never repeats in a predictable manner.
Converting .9999 into a Fraction
To convert .9999 into a fraction, we can use the following steps:
Step 1: Multiply by 10
Let's multiply .9999 by 10 to get 9.9999.
Step 2: Subtract the Original Number
Now, let's subtract .9999 from 9.9999 to get 9.
9.9999 - .9999 = 9
Step 3: Divide by 9
Finally, let's divide both sides of the equation by 9 to get:
(.9999) = 1
The Result
Surprisingly, the result shows that .9999 is equal to 1! This is a fascinating result, and it has many implications in mathematics.
Why is .9999 Equal to 1?
The reason why .9999 is equal to 1 is because the sequence of 9's goes on indefinitely. In other words, the decimal never terminates, and the sequence of 9's approaches 1 as the number of terms increases. This is a fundamental concept in mathematics, and it has many applications in calculus, algebra, and other areas of math.
Conclusion
In conclusion, .9999 can be converted into a fraction, and the result is surprisingly 1. This result has many implications in mathematics, and it is a fascinating example of how a non-terminating, non-repeating decimal can be equivalent to a simple integer.
