Question

One feet \(=12.0\) inches, one inch \(=2.54\) centimeters; write a program to compute inches and feet of \(76.2 \mathrm{cms}\).

Short answer

76.2 cm is approximately 2 feet and 6.0 inches.

Step-by-step solution

Convert Centimeters to Inches

We want to convert centimeters to inches using the relationship that 1 inch equals 2.54 centimeters. To find the number of inches in 76.2 centimeters, we use the formula: \[\text{Inches} = \frac{\text{Centimeters}}{\text{centimeters per inch}} = \frac{76.2}{2.54} \approx 30.0\text{ inches}\]

Convert Inches to Feet and Remaining Inches

Next, we convert the total inches into feet and remaining inches. We know that 1 foot equals 12 inches. So, to find the number of feet, divide the total inches by 12:\[\text{Feet} = \left\lfloor \frac{30.0}{12} \right\rfloor = 2\text{ feet}\]Now find the remaining inches: \[\text{Remaining Inches} = 30.0 - (2 \times 12) = 6.0\text{ inches}\]

Write a Program to Calculate the Conversion

To automate this conversion, write a simple program in Python: ```python # Constants cm_to_inch = 2.54 inch_to_foot = 12.0 # Input cm = 76.2 # Conversion inches = cm / cm_to_inch feet = int(inches // inch_to_foot) remaining_inches = inches % inch_to_foot # Output print(f"76.2 cm is approximately {feet} feet and {remaining_inches:.1f} inches.") ``` This program will calculate 76.2 cm as approximately 2 feet and 6.0 inches.

Key concepts

Python Programming

Python is an easy-to-learn, powerful programming language that can be used for a variety of applications, including mathematical and scientific calculations.
One of the many strengths of Python is its simplicity and readability, making it a suitable choice for both beginners and experienced programmers.

In the context of unit conversions, Python's syntax allows for clean and straightforward implementation of formulas and logic. In the example provided, a simple Python program is used to convert a measurement from centimeters to feet and inches.

This involves only a few steps:

• Define conversion constants (e.g., cm_to_inch, inch_to_foot).
• Perform arithmetic operations to execute the conversions.
• Print the results in a user-friendly format using f-strings.

This highlights Python's power to handle mathematical operations with minimal code and effort. With its built-in support for floating-point arithmetic and formatted output, complex problems can be simplified effectively.

Mathematical Calculations

Mathematical calculations are necessary for unit conversion tasks, especially when different measurement systems are involved.

In the provided exercise, converting units requires the following mathematical concepts:

• Division: Used to convert centimeters to inches by dividing the number of centimeters by 2.54 (the number of centimeters per inch).
• Floor Division: Used to calculate whole feet by dividing the total number of inches by 12 (the number of inches per foot).
• Modulus: Provides the remaining inches after calculating feet, by using the modulus operator to find the remainder from the division of total inches by 12.

These operations are crucial for converting between units and are easily handled in Python due to its mathematical capabilities.
It's important to note the choice of calculations: floor division helps obtain whole numbers (which makes sense for counting whole feet), whereas the modulus is ideal for finding what's left over (the extra inches). These calculations form the foundation for unit conversions in various programming scenarios.

Educational Programming Tasks

Educational programming tasks are designed to enhance understanding through practical, hands-on experience. They often involve real-world scenarios that require logical problem-solving and computational thinking.

The task of converting centimeters to feet and inches demonstrates several educational benefits:

• Application of Mathematical Concepts: Applying mathematical operations like division and modulus reinforces students’ arithmetic skills.
• Knowledge of Programming Constructs: Writing a program consolidates understanding of Python's basic syntax and data types.
• Problem-Solving Skills: Students learn how to interpret a problem, break it down into manageable steps, and implement a solution with programming logic.

These tasks can greatly improve both programming skills and mathematical understanding. They highlight the synergy between theory and practice, making knowledge more tangible and preparing students for more complex challenges in their academic and professional journeys.