Question
Multiple Representations Is the decimal form of StartFraction 10 Over 3 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 10 Over 3 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 10 Over 3 EndFraction
a rational number?
No
Yes
Answers
GPT-4o mini
Yes, the decimal form of \( \frac{10}{3} \) is a rational number.
To explain how we can determine this without finding the decimal form, we can use the definition of a rational number. A rational number is any number that can be expressed as the quotient of two integers (where the denominator is not zero).
In our case, \( \frac{10}{3} \) is already expressed as a quotient of two integers: 10 (the numerator) and 3 (the denominator). Since both the numerator and the denominator are integers, and the denominator is not zero, \( \frac{10}{3} \) meets the criteria for being a rational number.
Therefore, the answer is **Yes**, the decimal form of \( \frac{10}{3} \) is a rational number.
To explain how we can determine this without finding the decimal form, we can use the definition of a rational number. A rational number is any number that can be expressed as the quotient of two integers (where the denominator is not zero).
In our case, \( \frac{10}{3} \) is already expressed as a quotient of two integers: 10 (the numerator) and 3 (the denominator). Since both the numerator and the denominator are integers, and the denominator is not zero, \( \frac{10}{3} \) meets the criteria for being a rational number.
Therefore, the answer is **Yes**, the decimal form of \( \frac{10}{3} \) is a rational number.