Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational.

Part B: Find an irrational number that is between 7.7 and 7.9. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth.

Part A.

A rational number can be expressed as a quotient of two integers.

Therefore 78/10 = 39/5 = 0.78 represents a rational number between 7.7 and 7.9.

Answer: 39/5

Part B

An irrational number cannot be expressed as a quotient of two integers.

Let π*x = 7.8

Then x = 7.8/π = 2.483

Try 2.5*π = 7.854 which lies between 7.7 and 7.9

Answer: 7.85 (nearest hundredth)

Because this number is approximately equal to 2.5π, it is irrational because π is an irrational number.

The actual value of 2.5π = 7.8539816 ...