Question

Which of the following is a rational number between 5 and 514
?(1 point)
Responses

513
5 Start Fraction 1 over 3 end fraction

525
5 Start Fraction 2 over 5 end fraction

517
5 Start Fraction 1 over 7 end fraction

26−−√

Answer 1

To identify which of the given options is a rational number between 5 and 514, let's first convert the mixed fractions into improper fractions and check if they fall within this range.

1. **513**: This is an integer and clearly greater than 514.
2. **\(5 \frac{1}{3}\)**: This can be converted to an improper fraction \(5 \frac{1}{3} = \frac{16}{3} \approx 5.33\), which is greater than 5 but less than 514.
3. **525**: This is an integer and clearly greater than 514.
4. **\(5 \frac{2}{5}\)**: This can be converted to an improper fraction \(5 \frac{2}{5} = \frac{27}{5} = 5.4\), which is greater than 5 but less than 514.
5. **517**: This is an integer and clearly greater than 514.
6. **\(5 \frac{1}{7}\)**: This can be converted to an improper fraction \(5 \frac{1}{7} = \frac{36}{7} \approx 5.14\), which is greater than 5 but less than 514.
7. **\(26^{1/2}\) (or \(\sqrt{26}\))**: The approximate value of \(\sqrt{26} \approx 5.1\), which is greater than 5 but less than 514.

Now we summarize the options:

- \(513\), \(525\), and \(517\) are not within the range as they are greater than 514.
- The mixed fractions \(5 \frac{1}{3}\), \(5 \frac{2}{5}\), and \(5 \frac{1}{7}\) fall within the range \(5 < x < 514\).
- \(\sqrt{26}\) also falls within that range.

Thus, the rational numbers between 5 and 514 from the given options are:

- \(5 \frac{1}{3}\) (approximately 5.33)
- \(5 \frac{2}{5}\) (approximately 5.4)
- \(5 \frac{1}{7}\) (approximately 5.14)
- \(\sqrt{26}\) (approximately 5.1)

In conclusion, all mixed fraction options and \(\sqrt{26}\) are valid rational numbers between 5 and 514.