Question

(Converting Fabrenbeit to Celsius) Write a program that converts integer Fahrenheit temperatures from 0 to 212 degrees to floating-point Celsius temperatures with 3 digits of precision. Use the formula celsius \(=5.0 / 9.0^{*}\) ( fahrenheit -32 ); to perform the calculation. The output should be printed in two right-justified columns and the Celsius temperatures should be preceded by a sign for both positive and negative values.

Short answer

To convert from Fahrenheit to Celsius, use a loop to iterate from 0 to 212 degrees, convert each value using the formula Celsius = 5.0 / 9.0 * (Fahrenheit - 32), and display the results in a table with two right-justified columns, formatting Celsius values with 3 decimal places and sign prefixes.

Step-by-step solution

Understand the Conversion Formula

Recognize the formula to convert from Fahrenheit to Celsius: Celsius = 5.0 / 9.0 * (Fahrenheit - 32). This equation will be used in the program to calculate the Celsius value from the given Fahrenheit temperature.

Set up the Programming Environment

Choose a programming language suitable for the task, such as Python, Java, or C++. Set up the environment by opening a code editor and creating a new file to write the program.

Write a Loop to Iterate Through Temperatures

Create a loop that runs from 0 to 212 degrees Fahrenheit. This loop will go through each integer value within the range and convert it to Celsius.

Perform the Conversion within the Loop

Inside the loop, for each iteration (representing a Fahrenheit temperature), apply the conversion formula to obtain the Celsius temperature. The formula applied will be Celsius = 5.0 / 9.0 * (Fahrenheit - 32).

Format the Output

Ensure that the Celsius temperature is displayed with 3 digits of precision and that the Fahrenheit and converted Celsius values are right-justified within two columns. Prefix the Celsius temperatures with a plus or minus sign (+/-) according to whether they are positive or negative.

Output the Results

Print the Fahrenheit and corresponding Celsius temperatures in the specified format for each iteration of the loop to produce a table of converted temperatures.

Key concepts

C++ Programming

C++ is a versatile programming language well-suited for scientific computations like converting Fahrenheit to Celsius because it offers detailed control over numerical representations and performance.

When solving the given exercise, we'd start by creating a C++ program, utilizing a simple text editor or an integrated development environment (IDE). The first step in our program is to include headers such as #include <iostream> for console input and output and #include <iomanip> for formatting our output. Declaring the main function with int main() allows the program to be run.

In C++, you define variables to store the Fahrenheit and Celsius temperatures and use a for loop to iterate over the range of temperatures. Care must be taken to ensure that variables are of the correct type, such as using a float or double for the Celsius temperatures to support the required precision. Finally, std::fixed and std::setprecision from the <iomanip> library can be used to enforce the three digits of precision in the output.

Floating-Point Precision

In programming, floating-point precision is a measure of how accurately a computer can represent real numbers.

In the context of the Fahrenheit to Celsius conversion, precision is critical because it determines how accurately the Celsius temperature is calculated and displayed. C++ offers two primary floating-point types for storing such numbers: float and double. The float type is typically a 32-bit number with up to 7 digits of precision, while double provides a 64-bit number with roughly 15-16 digits of precision.

For our exercise, we can use the float type to ensure 3 digits of precision using the iomanip library functions std::fixed and std::setprecision(3). It's important to remember that the level of precision can affect the accuracy of your outcomes and may lead to rounding errors if not handled correctly.

Control Structures

Control structures in C++ determine the flow of execution of the program. They are pivotal when we need to execute a block of code multiple times or when a decision must be made in the code's logic.

In our temperature conversion program, we employ a for loop, a common control structure, to iterate over a sequence of temperatures from 0 to 212 degrees Fahrenheit. The syntax for this loop is for (initialization; condition; increment), where the initialization sets our starting point, condition sets when the loop should terminate, and increment updates our loop variable.

The body of the loop uses the conversion formula applied to each integer temperature within the range. This repetitive task is efficiently managed by the loop until all temperatures have been converted. With each iteration, the for loop executes the block of code that converts the current temperature and then outputs it in the desired format, demonstrating a practical application of control structures in a C++ program.