Question

What statements should you include in your program to ensure that, when a number of type double is output, it will be output in ordinary notation with three digits after the decimal point?

Short answer

Answer: You can use the "fixed" and "setprecision" manipulators from the iomanip library to achieve this. First, include the iostream and iomanip libraries. In the output statement, use std::fixed to display the number in decimal format and std::setprecision(3) to set the number of digits after the decimal point to 3. This will display the output in ordinary notation with three digits after the decimal point.

Step-by-step solution

Include iostream library

To start, make sure to include the iostream library, which allows us to perform input and output operations in C++. ```cpp #include ```

Include iomanip library

Also, you need to include the iomanip library, which contains the I/O manipulators we will use for this task. ```cpp #include ``` Step 2: Set Precision and Display Format

Set Precision

Use the "setprecision" manipulator in the output statement to set the number of digits to be displayed after the decimal point. In this case, it should be 3. ```cpp std::cout << std::setprecision(3); ```

Fix Display Format

Use the "fixed" manipulator in the output statement to ensure that the number is displayed in decimal format (as opposed to scientific notation). ```cpp std::cout << std::fixed; ``` Example Program: ```cpp #include #include int main() { double number = 123.456789; // Display number with 3 digits after the decimal point in ordinary notation std::cout << std::fixed << std::setprecision(3) << number << std::endl; return 0; } ```

Key concepts

The iostream Library

The `iostream` library is essential for performing input and output operations in C++. By including the `iostream` library, you gain access to standard streams like `std::cin`, `std::cout`, `std::cerr`, and `std::clog`. These streams simplify the process of reading from and writing to the console.
When you use `#include`, it allows your program to utilize these streams efficiently, making them a staple in almost any C++ program that requires user interaction or output display.
Typically, `std::cout` is used to display data on the screen, while `std::cin` is used to receive user input. Ensure you include the `iostream` library at the top of your program to avoid runtime errors related to the input/output operations.
In the example provided, `std::cout` is employed to output the formatted number to the screen, which is crucial for understanding number formatting in C++.

The iomanip Library

The `iomanip` library is another vital component when it comes to formatting output in C++. This library includes a variety of output manipulators that help control different aspects of how data is displayed.
By including `#include`, you get access to manipulators such as `std::setprecision`, `std::setw`, `std::fixed`, and more. Each of these provides unique functionality that can change the presentation of your output.
For example, `std::setw` can specify the width of an output stream, `std::setprecision` sets the number of digits displayed, and `std::fixed` ensures numbers are displayed in fixed-point notation.
Having the `iomanip` library included in your code enables you to handle complex formatting demands with ease, allowing for greater precision and clarity in the output.

The setprecision Manipulator

The `setprecision` manipulator in C++ plays a crucial role in controlling the number of significant digits or decimal places that are displayed in the output of floating-point numbers. By default, the precision might not align with your specific needs, which is where `setprecision` comes into play.
To use `setprecision`, you include it in the output statement to dictate how many digits should be displayed after the decimal point. For instance, `std::cout << std::setprecision(3);` sets the precision to three digits.
Do note that when combined with `std::fixed`, it limits the number of digits after the decimal to three, offering a clear and specified presentation. However, without `std::fixed`, `setprecision` would adjust the overall number of significant digits.
It's a convenient tool for formatting numerical output, ensuring data is displayed with the precision necessary for your calculations.

The fixed Manipulator

In C++, the `fixed` manipulator is specifically used to control the notation format of floating-point numbers. By default, numbers might be displayed in scientific notation if they're large or small enough. Utilizing `std::fixed` forces these numbers into a fixed-point representation instead.
When you apply `std::fixed` before setting up any precision with `std::setprecision`, it ensures that the output is always shown in a non-scientific, decimal format. This is especially useful in financial calculations or any situation where a consistent notation is essential.
In combination with `std::setprecision`, it provides granular control over how values are printed. For example, using `std::cout << std::fixed << std::setprecision(3);` guarantees that the number appears with exactly three digits after the decimal point, enhancing readability and precision in the output.
By keeping your outputs in a readable and fixed-point format, you improve the clarity of the data presented, making your programs more user-friendly.