.9 Repeating as a Fraction in Simplest Form
Have you ever wondered how to convert the repeating decimal .9 into a fraction in its simplest form? If so, you're in the right place! In this article, we'll explore the process of converting .9 repeating into a fraction.
What is .9 Repeating?
.9 repeating is a decimal that has a sequence of 9s that repeats indefinitely. It can be written as:
.9, .99, .999, .9999, ...
Converting .9 Repeating to a Fraction
To convert .9 repeating into a fraction, we can use a simple trick. Let's start by letting x = .9 repeating.
Since .9 repeating has an infinite sequence of 9s, we can multiply both sides of the equation by 10 to get:
10x = 9.9 repeating
Next, we'll subtract x from both sides of the equation to get:
9x = 9
Now, we can divide both sides of the equation by 9 to solve for x:
x = 1
So, .9 repeating is equal to 1! But we're not done yet. We still need to express it as a fraction in its simplest form.
Simplest Form of .9 Repeating as a Fraction
The simplest form of .9 repeating as a fraction is:
1/1
That's right, .9 repeating is equal to the fraction 1/1, which simplifies to 1.
Conclusion
In this article, we've learned how to convert .9 repeating into a fraction in its simplest form. By using a simple trick and performing a few algebraic manipulations, we've shown that .9 repeating is equal to 1, or 1/1 in fraction form.
I hope this helps!
