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

Question

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(1 point)
Responses

26−−√

square root of 26
518
51 eighth
525
52 fifths
513

Answer 1

To determine which of the provided options is a rational number between 5 and 514, we'll evaluate each option:

1. √26: This is an irrational number. The decimal approximation is approximately 5.099, which is between 5 and 514 but not a rational number.

2. 518: This number is greater than 514, so it does not fall within the range.

3. 51/8: This is a rational number.

   • Calculating: \( 51 ÷ 8 = 6.375 \), which is greater than 5 and less than 514.

4. 525: This number is also greater than 514, so it does not fall within the range.

5. 52/5: This is a rational number.

   • Calculating: \( 52 ÷ 5 = 10.4 \), which is greater than 5 and less than 514.

6. 513: This number is less than 514 but still greater than 5.

Given the evaluations, the rational numbers that fall between 5 and 514 are 51/8 and 52/5. However, since the question asks for a single rational number, the best choice is:

51/8.