.2 Repeating as a Fraction in Simplest Form
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is .2 repeating, which can be written as 0.222222... . But have you ever wondered what .2 repeating is as a fraction in simplest form? In this article, we'll explore the answer to this question.
Converting .2 Repeating to a Fraction
To convert .2 repeating to a fraction, we can use the following steps:
- Let x = 0.222222... (the repeating decimal)
- Multiply both sides of the equation by 10 to get 10x = 2.222222...
- Subtract x from both sides to get 9x = 2
- Divide both sides by 9 to get x = 2/9
Therefore, .2 repeating is equal to 2/9 as a fraction in simplest form.
Proof
To prove that .2 repeating is indeed equal to 2/9, we can use the following calculation:
.2 repeating = 0.222222... = (2/10) + (2/100) + (2/1000) + ...
Using the formula for an infinite geometric series, we can rewrite this as:
.2 repeating = (2/10) / (1 - 1/10) = 2/9
This confirms that .2 repeating is equal to 2/9 as a fraction in simplest form.
Conclusion
In conclusion, .2 repeating is equal to 2/9 as a fraction in simplest form. This is a useful conversion to know, as it can help in solving various mathematical problems involving repeating decimals. By following the steps outlined above, you can convert any repeating decimal to a fraction in simplest form.
