Question

(Converting Fabrenheit Temperature to Celsius) Write a program that converts integer Fahrenheit temperatures from 0 to 212 degrees to floating-point Celsius temperatures with three digits of precision. Use the formula celsius \(=5.0 / 9.0\) a ( fahrenheit -32 ); to perform the calculation. The output should be printed in two right-justified columns of 10 characters each, and the Celsius temperatures should be preceded by a sign for both positive and negative values.

Short answer

To convert 0 to 212°F to Celsius with precision, loop over the Fahrenheit range, apply the conversion formula, and print formatted output with right-justified columns.

Step-by-step solution

Initialize Temperature Ranges

Start by setting a range for Fahrenheit temperatures, typically from 0 to 212 as specified, to be converted into Celsius.

Apply the Formula

Use the formula for conversion: \[\text{celsius} = \frac{5.0}{9.0} \times (\text{fahrenheit} - 32)\]This formula takes the Fahrenheit temperature, subtracts 32, and multiplies the result by \( \frac{5.0}{9.0} \) to convert it to Celsius.

Format the Output

Ensure the Celsius temperature is a floating-point number with three decimal points of precision. Use string formatting to print two columns: Fahrenheit values right-justified and Celsius values also right-justified with a sign prefix ('+' or '-'). Each column should have a width of 10 characters.

Implement the Program

Create a loop to iterate over the Fahrenheit range, converting each value to Celsius and printing them in the specified format. Make sure to include code to handle the sign and the formatting of the output for alignment.

Key concepts

Floating-Point Arithmetic

Floating-point arithmetic is essential in scientific and engineering calculations. It enables the representation of fractional numbers where precision is needed. For instance, when converting temperatures using the Celsius formula, precision is crucial to ensure accuracy. When working with the conversion formula:\[ \text{celsius} = \frac{5.0}{9.0} \times (\text{fahrenheit} - 32) \]Notice that the numbers 5.0 and 9.0 are written as floating-point numbers (decimals). This ensures that the division and subsequent multiplication yield a floating-point result. This type of arithmetic helps avoid errors that could accumulate if integer division were used, providing a much more accurate and precise computation of Celsius temperatures. For many applications, proper handling of decimal precision keeps calculations consistent and reliable.

String Formatting

String formatting in Java allows developers to control how different types of data are presented in the output. For temperature conversion, it’s important to format the Celsius results correctly, especially since precision affects readability and usability of data. Using string formatting, we specify:

• Columns are right-justified, ensuring alignment for clarity.
• Three decimal places are shown for the Celsius values.
• The sign ('+' or '-') precedes the Celsius values.

For example, in code, you might use `String.format()` to achieve these requirements, ensuring both the Fahrenheit and Celsius values are aligned in columns each 10 characters wide. This attention to detail is not just about aesthetics; it's about presenting data clearly and understandably to anyone who views the output.

Loop Implementation

The implementation of loops in Java allows us to automate repetitive tasks very efficiently. In our temperature conversion example, loops help process every Fahrenheit degree incrementally from 0 to 212. The common structure for loops includes:

• Initialization: Start with the initial value of Fahrenheit.
• Condition: Continue the loop as long as the Fahrenheit value is within the specified range.
• Increment: Increase the Fahrenheit value by 1 each iteration.

Inside the loop, the conversion formula is applied and formatted results are printed. Using loops not only saves time but also minimizes errors since the code executes the same set of instructions iteratively, eliminating manual input for each temperature conversion.

Temperature Ranges

In temperature conversion exercises, defining a clear range for the values to be converted is fundamental. The specified range of 0 to 212 degrees Fahrenheit is significant for several reasons.

• It represents the typical boiling point of water (212°F) in atmospheric conditions.
• It covers the range of most everyday temperatures one might encounter.
• A defined range helps with structuring loops, ensuring the program executes predictably and within bounds.

By clearly setting these bounds, the program remains efficient and logical, providing users with an expected set of results. Understanding the context of these ranges also allows programmers to build systems that reflect real-world conditions and constraints more accurately.