A rational number is a number that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
The options provided are:
- 513
- 5
- \( \frac{1}{3} \)
- \( \sqrt{26} \)
- 525
- \( \frac{2}{5} \)
- 517
Out of these options, we need to identify which are rational numbers that fall between 5 and 514.
- 513 is rational and is between 5 and 514.
- 5 is not between 5 and 514, as it is equal to 5.
- \( \frac{1}{3} \) is a rational number, but it is not between 5 and 514.
- \( \sqrt{26} \) is an irrational number.
- 525 is not between 5 and 514, as it exceeds 514.
- \( \frac{2}{5} \) is a rational number, but it is not between 5 and 514.
- 517 is not between 5 and 514, as it exceeds 514.
The only rational number between 5 and 514 from the provided options is 513.