0.9 Repeating as a Fraction in Simplest Form
What is 0.9 Repeating?
0.9 repeating, also known as 0.9~, is a decimal that has a repeating pattern of 9s. It is a non-terminating, recurring decimal that goes on indefinitely in a repeating cycle. In other words, 0.9 repeating is a decimal that has an infinite number of 9s.
Converting 0.9 Repeating to a Fraction
To convert 0.9 repeating to a fraction, we can use the following steps:
- Let x = 0.9~
- Multiply both sides by 10 to get 10x = 9.9~
- Subtract x from both sides to get 9x = 9
- Divide both sides by 9 to get x = 1
So, 0.9 repeating is equal to 1.
Simplifying the Fraction
Since 0.9 repeating is equal to 1, it is already in its simplest form. There is no need to simplify the fraction further.
Conclusion
In conclusion, 0.9 repeating is equal to 1 in its simplest form. This means that the decimal 0.9~, which seems like a complicated and endless string of 9s, is actually equal to a simple whole number.
