.08 Repeating as a Fraction in Simplest Form
What is .08 Repeating?
.08 repeating, also known as .080808..., is a non-terminating, repeating decimal. This means that the sequence of digits ".08" repeats indefinitely.
Converting .08 Repeating to a Fraction
To convert .08 repeating to a fraction, we can use the following steps:
- Let x = .080808...
- Multiply both sides by 100 to get 100x = 8.080808...
- Subtract x from both sides to get 99x = 8
- Divide both sides by 99 to get x = 8/99
Therefore, .08 repeating can be written as a fraction in simplest form as:
8/99
Proof
To prove that 8/99 is the correct fraction, we can convert it back to a decimal:
8 ÷ 99 = 0.080808...
As we can see, the decimal equivalent of 8/99 is indeed .08 repeating.
Conclusion
In conclusion, .08 repeating can be written as a fraction in simplest form as 8/99. This conversion can be achieved using the steps outlined above, which involve multiplying, subtracting, and dividing to isolate the repeating decimal pattern.
