Question

rounds \(x\) to the hundredths position (the second position to the right of the decimal point). Write a program that defines four functions to round a number \(x\) in various ways: a. roundToInteger ( number ) b. roundToTenths ( number ) C. roundToHundredths ( number ) d. roundToThousandths ( number ) For each value read, your program should print the original value, the number rounded to the nearest integer, the number rounded to the nearest tenth, the number rounded to the nearest hundredth and the number rounded to the nearest thousandth.

Short answer

Define four rounding functions and use them to round and print the input number at different decimal places.

Step-by-step solution

Define the Function roundToInteger

In this step, you'll define a function named `roundToInteger` that takes a number as an argument and returns that number rounded to the nearest integer. This can be done using Python's built-in `round` function. Here's the code: ```python def roundToInteger(number): return round(number) ```

Define the Function roundToTenths

Next, define a function named `roundToTenths`. This function will take a number as an argument and round it to the nearest tenth (one decimal place). You can achieve this by specifying 1 as the second parameter to the `round` function: ```python def roundToTenths(number): return round(number, 1) ```

Define the Function roundToHundredths

Define a function named `roundToHundredths` that rounds a number to the nearest hundredth (two decimal places). Use the `round` function with 2 as the second argument: ```python def roundToHundredths(number): return round(number, 2) ```

Define the Function roundToThousandths

Create a function named `roundToThousandths` to round a number to the nearest thousandth (three decimal places). The `round` function should be passed 3 as the second argument: ```python def roundToThousandths(number): return round(number, 3) ```

Implement Reading, Rounding, and Printing

Finally, implement the logic to read values, round them using the defined functions, and print the results. Here's an example: ```python number = float(input("Enter a number: ")) print(f"Original value: {number}") print(f"Rounded to nearest integer: {roundToInteger(number)}") print(f"Rounded to nearest tenth: {roundToTenths(number)}") print(f"Rounded to nearest hundredth: {roundToHundredths(number)}") print(f"Rounded to nearest thousandth: {roundToThousandths(number)}") ```

Key concepts

rounding to integer

Rounding to the nearest integer is a fundamental concept in programming that transforms a floating-point number into a whole number. This process is crucial in scenarios where fractional values need to be eliminated or when approximate values are sufficient. The general rule for rounding to an integer is to check the digit immediately after the decimal point. If this digit is 5 or greater, the number is rounded up. Otherwise, the number is rounded down.

For example, a number like 4.6 would be rounded to 5, while 4.4 would become 4. In C++, you can use the `round()` function from the `` library to achieve this. This function will return the nearest integer as a double. Thus, using `round()` is simple and efficient for rounding numbers in C++. It’s as easy as calling `round(your_number)`, where `your_number` is the value you wish to round.

rounding to decimal places

Rounding numbers to a specified number of decimal places is a common requirement when we need precise values without unnecessary fractional digits. This concept involves choosing how many digits should remain after the decimal point. Let's explore how you can do this in C++.

C++ provides several ways to round numbers to decimal places, but one common method uses the `round()` function in combination with multiplication and division. For example, to round a number to the tenths place (one decimal), you would multiply the number by 10, apply the `round()` function, and then divide by 10. This effectively shifts the decimal point, rounds it to the nearest whole number, and shifts it back. Here’s how it looks for one decimal place:

• Multiply the number by 10: `number * 10`
• Round the result: `round(result)`
• Divide by 10: `result / 10`

This pattern repeats by multiplying and dividing by powers of 10, such as 100 for hundredths, or 1000 for thousandths. Each of these can be encapsulated into a simple function.

defining functions in C++

Defining functions in C++ is an essential skill that allows you to write reusable and modular code. A function is a block of code designed to perform a specific task, and it is defined once but can be used repeatedly. In C++, a function definition consists of a return type, a name, a parameter list, and a block of code.

Here’s a basic template to define a function: ```cpp returnType functionName(parameterList) { // function body } ```

• returnType: Specifies what type of value is returned (like `void` for no return or `int` for integers).
• functionName: A unique identifier for the function.
• parameterList: Contains input values for the function in parentheses.

For example, a function to add two numbers would look like this: ```cpp int addNumbers(int a, int b) { return a + b; } ``` To call this function, you would simply use `addNumbers(3, 5)`, which would return 8. Functions enhance readability and allow for better organization of code, making it easier to manage large programs.

input and output in programming

Understanding input and output (I/O) operations is vital for interacting with users and other data sources in C++. This interaction typically happens through the console using streams provided by the C++ Standard Library.

For input, C++ uses the `cin` object to take data from the standard input, which usually means the keyboard. The `>>` operator is used to read data into a variable: ```cpp int number; std::cout << "Enter a number: "; std::cin >> number; ``` Here, the prompt is displayed using `cout`, then `cin` waits for the user to provide input. For output, the `cout` object is used with the `<<` operator to stream data to the standard output, usually the screen: ```cpp std::cout << "The number you entered is: " << number << std::endl; ```

• `cout` and `cin` are part of the `iostream` library, which must be included at the start of the program with `#include `.
• `endl` is used to insert a newline into the output, making it user-friendly.

Proper handling of I/O operations ensures that programs are responsive and user-friendly, facilitating all user interactions smoothly.