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 26−−√ start root 26 end root 525 5 Start Fraction 2 over 5 end fraction 517

Answer 1

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:

1. 513
2. 5
3. \( \frac{1}{3} \)
4. \( \sqrt{26} \)
5. 525
6. \( \frac{2}{5} \)
7. 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**.