Which of the following is a rational number between 5 and 514

Question

?(1 point)
Responses

517
5 Start Fraction 1 over 7 end fraction

513
5 Start Fraction 1 over 3 end fraction

525
5 Start Fraction 2 over 5 end fraction

26−−√

Answer 1

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

1. 517 - This is greater than 514.
2. 5 (1/7) - This can be written as \(5 + \frac{1}{7} = 5.142857...\), which is between 5 and 514.
3. 513 - This is greater than 514.
4. 5 (1/3) - This can be written as \(5 + \frac{1}{3} = 5.3333...\), which is also between 5 and 514.
5. 525 - This is greater than 514.
6. \( \sqrt{26} \) - This is approximately \(5.099\), which is also between 5 and 514.

All of the following are rational numbers between 5 and 514:

• \(5 \frac{1}{7}\)
• \(5 \frac{1}{3}\)
• \( \sqrt{26} \)

However, since you only need to identify one such number, the option 5 (1/7) is a suitable choice.