Question

Which of the following is a rational number between 5 and 514 ?(1 point) Responses 525 5 Start Fraction 2 over 5 end fraction 513 5 Start Fraction 1 over 3 end fraction 517 5 Start Fraction 1 over 7 end fraction 26−−√

Answer 1

To determine which of the given options is a rational number between 5 and 514, we can analyze each option:

1. **525** - This is not between 5 and 514.
2. **5 Start Fraction 2 over 5 end fraction** - This is equivalent to \( 5 + \frac{2}{5} = 5.4 \), which is between 5 and 514.
3. **513** - This is also not between 5 and 514 since it is on the upper limit.
4. **5 Start Fraction 1 over 3 end fraction** - This is equivalent to \( 5 + \frac{1}{3} \approx 5.333 \), which is between 5 and 514.
5. **517** - This is not between 5 and 514.
6. **5 Start Fraction 1 over 7 end fraction** - This is equivalent to \( 5 + \frac{1}{7} \approx 5.142857 \), which is also between 5 and 514.
7. **26−−√** - The square root of 26 is approximately 5.099, which is between 5 and 514 but is not a simple rational number.

The options that are rational numbers between 5 and 514 are:
- \( 5 + \frac{2}{5} \) (5.4)
- \( 5 + \frac{1}{3} \) (approximately 5.333)
- \( 5 + \frac{1}{7} \) (approximately 5.142857)

Thus, the correct responses are **5 Start Fraction 2 over 5 end fraction**, **5 Start Fraction 1 over 3 end fraction**, and **5 Start Fraction 1 over 7 end fraction**.