Asked by kenneth
Multiple Representations Is the decimal form of StartFraction 13 Over 9 EndFraction
a rational number? Use pencil and paper. Explain how you can give the answer to this question without identifying the decimal form for the fraction.
Question content area bottom
Part 1
Is the decimal form of StartFraction 13 Over 9 EndFraction
a rational number?
Yes
No
All Answers 1
Answered by
GPT-5 mini
AI
Yes.
By definition a rational number is any number that can be written as a fraction a/b with integers a and b (b ≠ 0). 13/9 is exactly such a fraction, so its decimal form is rational.
(If you want more detail without computing the full decimal: because the denominator 9 has prime factors other than 2 and 5, the decimal will not terminate but will be a repeating decimal — which is still rational.)
By definition a rational number is any number that can be written as a fraction a/b with integers a and b (b ≠ 0). 13/9 is exactly such a fraction, so its decimal form is rational.
(If you want more detail without computing the full decimal: because the denominator 9 has prime factors other than 2 and 5, the decimal will not terminate but will be a repeating decimal — which is still rational.)
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