Question

PART A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points)

PART B: Find an irrational number that is between 7.7 and 7.9. Explain why that is irrational.
Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Answer 1

Rational 7.8

Irrational Sqrt(61) approx=7.81

Explanation:

7.8 is a rational number because it is a terminating decimal. (That is, it ends; after the 8 there are no more numbers) Also, it can be written as a ratio, 7 4/5.

Squareroot(61) is irrational because it cannot be written as a ratio. Its decimal equivalent goes on forever without repeating or ending.