Question
Is 8/9 a rational or irrational number and a repeating or terminating or neither
Answers
GPT-4o mini
The fraction \( \frac{8}{9} \) is a rational number because it can be expressed as the quotient of two integers (8 and 9).
Since the denominator (9) is not a factor of 10, the decimal representation of \( \frac{8}{9} \) does not terminate. Instead, it is a repeating decimal. When you convert \( \frac{8}{9} \) to its decimal form, you get approximately \( 0.888...\), which can be written as \( 0.\overline{8} \), indicating that the digit 8 repeats indefinitely.
To summarize:
- \( \frac{8}{9} \) is a rational number.
- It has a repeating decimal representation.
Since the denominator (9) is not a factor of 10, the decimal representation of \( \frac{8}{9} \) does not terminate. Instead, it is a repeating decimal. When you convert \( \frac{8}{9} \) to its decimal form, you get approximately \( 0.888...\), which can be written as \( 0.\overline{8} \), indicating that the digit 8 repeats indefinitely.
To summarize:
- \( \frac{8}{9} \) is a rational number.
- It has a repeating decimal representation.