Question
Which numbers are rational? Check the three that apply.
Responses
\/104
pi
\/16
\/21
7/23
3.8
Responses
\/104
pi
\/16
\/21
7/23
3.8
Answers
GPT-4o mini
To determine which numbers are rational, recall that a rational number is any number that can be expressed as the quotient or fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
Now, let's evaluate the given options:
1. **\( \sqrt{104} \)**: This is an irrational number because it cannot be simplified into a fraction of two integers.
2. **\( \pi \)**: This is also an irrational number and cannot be expressed as a fraction.
3. **\( \sqrt{16} \)**: This simplifies to 4, a whole number, which is rational (since it can be expressed as \( \frac{4}{1} \)).
4. **\( \sqrt{21} \)**: This is an irrational number because it cannot be simplified into a fraction of two integers.
5. **\( \frac{7}{23} \)**: This is a fraction of two integers, making it a rational number.
6. **3.8**: This can be expressed as \( \frac{38}{10} \) or \( \frac{19}{5} \), thus it is also a rational number.
The three numbers that are rational from the given options are:
- \( \sqrt{16} \)
- \( \frac{7}{23} \)
- 3.8
Now, let's evaluate the given options:
1. **\( \sqrt{104} \)**: This is an irrational number because it cannot be simplified into a fraction of two integers.
2. **\( \pi \)**: This is also an irrational number and cannot be expressed as a fraction.
3. **\( \sqrt{16} \)**: This simplifies to 4, a whole number, which is rational (since it can be expressed as \( \frac{4}{1} \)).
4. **\( \sqrt{21} \)**: This is an irrational number because it cannot be simplified into a fraction of two integers.
5. **\( \frac{7}{23} \)**: This is a fraction of two integers, making it a rational number.
6. **3.8**: This can be expressed as \( \frac{38}{10} \) or \( \frac{19}{5} \), thus it is also a rational number.
The three numbers that are rational from the given options are:
- \( \sqrt{16} \)
- \( \frac{7}{23} \)
- 3.8