What is a rational number with a denominator of 7 that is between 7–√ and

Answer 1

To find a rational number with a denominator of 7 that is between 7–√ and 5, we need to convert the decimal values of these numbers to fractions with a denominator of 7.

We know that 7–√ is approximately 7–2.645751 or 4.354249. Let's convert it to a fraction with a denominator of 7:

7–√ ≈ 4.354249 ≈ 4 + 35/1000 = 4 + 35/10,000 = (40,000 + 35)/10,000 = 40,035/10,000

The rational number between 7–√ and 5 would have a numerator smaller than 40,035 and a denominator of 7. Let's choose a value such as 40,010 to ensure it falls between these two numbers:

Rational number = 40,010/10,000 = 4 + 10/1000 = 4 + 1/100 = 4 + 1/10,000 = 4 + 0.0001 ≈ 4.0001

Therefore, a rational number with a denominator of 7 that is between 7–√ and 5 is approximately 4.0001.