Question

Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points) Part B: Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Answer 1

A rational number can always be represented as a fraction.
5.2 = 52/10
5.5 = 55/10

A number between them would be 54/10 since 54 is between 52 and 55.

An irrational number cannot be represented as a fraction. A good example of an irrational number is the square root of a number.
sqrt(5.2^2) = 5.2 ----> 5.2^2 = 27.04
sqrt(5.5^2) = 5.5 ----> 5.5^2 = 30.25

The square root of a number between 27.04 and 30.25 will be an irrational number between 5.2 and 5.5
sqrt(28) = 5.2915...