Question
Multiple Representations Is the decimal form of StartFraction 19 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 19 Over 9 EndFraction
a rational number?
No
Yes
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 19 Over 9 EndFraction
a rational number?
No
Yes
Answers
GPT-4o mini
Yes, the decimal form of \(\frac{19}{9}\) is a rational number.
### Explanation:
A rational number is defined as any number that can be expressed as the quotient (or fraction) of two integers, where the denominator is not zero. In this case, \(\frac{19}{9}\) is already in the form of a fraction where 19 is the numerator (an integer) and 9 is the denominator (also an integer and not zero).
Since \(\frac{19}{9}\) is a fraction of two integers, it is inherently a rational number, regardless of what its decimal form might be. Therefore, without needing to convert \(\frac{19}{9}\) to its decimal form, we can definitively say that it is a rational number.
### Explanation:
A rational number is defined as any number that can be expressed as the quotient (or fraction) of two integers, where the denominator is not zero. In this case, \(\frac{19}{9}\) is already in the form of a fraction where 19 is the numerator (an integer) and 9 is the denominator (also an integer and not zero).
Since \(\frac{19}{9}\) is a fraction of two integers, it is inherently a rational number, regardless of what its decimal form might be. Therefore, without needing to convert \(\frac{19}{9}\) to its decimal form, we can definitively say that it is a rational number.