Numbers Between Rational Numbers Discussion

Question

Math 8 Q1 (Pre-Algebra) / The Number System

In your journal, you identified careers that involve irrational numbers. You brainstormed or researched jobs that use pi or Euler’s number to do their work.
Imagine that your friend loves to plan parties, and he wants to be an event planner someday. He does not think he needs to know how to find a number between two rational numbers. He also says he will never use pi again in his life after math class. You think of some of the tasks he might need to do as an event planner:

Choose a round table that is the correct size to fit six people

Answer 1

As an event planner, your friend may need to consider the size and shape of tables for different events. When it comes to choosing a round table that can fit six people, the concept of finding a number between two rational numbers can be useful.

Let's say your friend has two options for round tables: one with a diameter of 48 inches and one with a diameter of 60 inches. Both options are rational numbers because they can be expressed as a fraction (48/1 and 60/1).

To determine which table is the correct size to fit six people, your friend would need to consider the space each person would occupy. Typically, it is recommended to allocate around 24 inches per person for a comfortable seating arrangement.

If your friend chooses the smaller table with a diameter of 48 inches, the radius would be 48/2 = 24 inches. Considering each person would need 24 inches of space, the total space occupied by six people would be 24 inches * 6 = 144 inches. Since the diameter of the table (48 inches) is greater than the space required (144 inches), this table would be too small to comfortably fit six people.

On the other hand, if your friend chooses the larger table with a diameter of 60 inches, the radius would be 60/2 = 30 inches. With the same calculation, the total space occupied by six people would be 24 inches * 6 = 144 inches. In this case, the diameter of the table (60 inches) is larger than the required space (144 inches), indicating that this table would be a suitable size to accommodate six people comfortably.

By understanding how to find a number between two rational numbers, your friend can make informed decisions about table sizes and ensure a comfortable seating arrangement for the guests at the parties he plans.