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

Answer 1

To find a rational number between 5 and 514, we need to evaluate the given options:

1. 517 - This is greater than 514.
2. 5 \( \frac{1}{7} \) - This is equal to \( 5 + \frac{1}{7} = \frac{36}{7} \) or approximately 5.14, which is greater than 5 but less than 514.
3. 525 - This is greater than 514.
4. 5 \( \frac{2}{5} \) - This is equal to \( 5 + \frac{2}{5} = \frac{27}{5} \) or approximately 5.4, which is greater than 5 but less than 514.
5. \( \sqrt{26} \) - This is not a rational number, as the square root of 26 is irrational and approximately equal to 5.1.
6. 513 - This is greater than 514.
7. 5 \( \frac{1}{3} \) - This is equal to \( 5 + \frac{1}{3} = \frac{16}{3} \) or approximately 5.33, which is greater than 5 but less than 514.

From the evaluations, the following options are rational numbers between 5 and 514:

• 5 \( \frac{1}{7} \)
• 5 \( \frac{2}{5} \)
• 5 \( \frac{1}{3} \)

In summary, all three fractions \( (5 \frac{1}{7}, 5 \frac{2}{5}, 5 \frac{1}{3}) \) are valid rational numbers between 5 and 514.