Numbers Between Rational Numbers Discussion
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
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.
As an event planner, choosing a round table that is the correct size to fit six people involves finding a diameter or radius that can accommodate six chairs. To do this, your friend would need to know how to find a number between two rational numbers. This is because the measurement needed may not be a whole number or an exact fraction.
To find a number between two rational numbers, your friend could follow these steps:
Step 1: Determine the range of possible table sizes. Your friend could start by identifying the minimum and maximum table diameters or radii that would be too small or too large for six people. For example, an extremely small table with a diameter of 1 inch or a large table with a diameter of 15 feet would not be suitable.
Step 2: Choose reasonable rational numbers that fall within the range determined in Step 1. Let's say your friend determines that a table diameter between 3 feet and 8 feet would be appropriate. He could choose two rational numbers, such as 4 feet and 6 feet, as a starting point.
Step 3: Find a number between the two chosen rational numbers. To do this, your friend could take the average of the chosen numbers. Adding the two numbers and dividing by 2 would give him a number that falls between the two chosen rational numbers.
For example, to find a number between 4 feet and 6 feet, your friend could add them together: 4 + 6 = 10. Then, he would divide 10 by 2: 10 ÷ 2 = 5. So, 5 feet would be a rational number that falls between 4 feet and 6 feet.
Step 4: Evaluate if the number found in Step 3 is suitable for the specific purpose. Your friend should consider if 5 feet is an appropriate table diameter for fitting six people comfortably. If the answer is yes, then he can proceed with selecting a table of that size. If not, he may need to repeat the process by choosing different rational numbers and finding a new number between them.
It's worth noting that while pi might not be directly used in this particular task, having a general understanding of irrational numbers, like pi, can be beneficial for overall mathematical comprehension and problem-solving skills in various career paths.