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 5 Start Fraction 1 over 7 end fraction

Answer 1

A rational number is any number that can be expressed as a fraction \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\).

Now, let's analyze the given options to see which ones are rational numbers between 5 and 514:

1. **513**: This is a whole number (and can be expressed as \(\frac{513}{1}\)), and it is between 5 and 514.
2. **5**: This is a whole number, but it's not between 5 and 514 (it's equal to 5).
3. **\(\frac{1}{3}\)**: This is a rational number, but it is not between 5 and 514.
4. **\(\sqrt{26}\)**: This is an irrational number (it cannot be expressed as a fraction).
5. **525**: This is greater than 514, so it doesn't fit.
6. **\(\frac{2}{5}\)**: This is a rational number but is not between 5 and 514.
7. **517**: This is a whole number (and can be expressed as \(\frac{517}{1}\)), and it is between 5 and 514.
8. **\(\frac{1}{7}\)**: This is a rational number, but it is not between 5 and 514.

The rational numbers from the choices provided that are between 5 and 514 are **513** and **517**.