Question

Math.floor may be used to round a number to a specific decimal place. The statement y = Math.floor( x * 10 + 0.5 ) / 10; rounds x to the tenths position (i.e., the first position to the right of the decimal point). The statement y = Math.floor( x * 100 + 0.5 ) / 100; rounds x to the hundredths position (i.e., the second position to the right of the decimal point). Write an application that defines four methods for rounding 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 display the original value, the number rounded to the nearest integer, the number rounded to the nearest tenth, the number rounded to the nearest hun- dredth and the number rounded to the nearest thousandth.

Short answer

Create rounding methods using `Math.floor` and display rounded results.

Step-by-step solution

Understanding Rounding Functions

We need to create functions that will round a given number to various positions: nearest integer, tenths, hundredths, and thousandths. We use a formula involving `Math.floor` and multiplication to achieve this for each required position.

Defining the roundToInteger Function

To round to the nearest integer, multiply the number by 1 (which is redundant), add 0.5, apply `Math.floor` to this sum, then divide by 1 (again redundant). This gives us the integer closest to the original number.

Defining the roundToTenths Function

For rounding to the nearest tenth, multiply the number by 10, add 0.5, and apply `Math.floor` to this result. Finally, divide by 10. Formally, the code can be `return Math.floor(number * 10 + 0.5) / 10;`.

Defining the roundToHundredths Function

To round to the nearest hundredth, multiply the number by 100, add 0.5, and apply `Math.floor`. Then, divide the result by 100. The code can be written as `return Math.floor(number * 100 + 0.5) / 100;`.

Defining the roundToThousandths Function

Rounding to the nearest thousandth involves multiplying the number by 1000, adding 0.5, applying `Math.floor`, and dividing by 1000. The implementation is: `return Math.floor(number * 1000 + 0.5) / 1000;`.

Program Structure and Output Display

Create a program that reads a number and calls each of the rounding methods defined. The program should then print the original number, along with its rounded values to integer, tenths, hundredths, and thousandths places, in a friendly format.

Key concepts

Math.floor

In Java programming, the `Math.floor` function is a crucial tool for rounding numbers down to the nearest whole integer. This function always returns the largest integer that is less than or equal to the original number.
This behavior is often used in rounding applications where precise control over decimal places is needed.
For instance, if you encounter a fractional number like 3.7, `Math.floor(3.7)` will return 3, effectively removing the decimal component. To control rounding to specific decimal places, you apply
multiplication and division in concert with `Math.floor`—a neat trick that shifts the decimal point, performs the floor operation, and then shifts it back.

• Multiply the number to move the target decimal place to the integer zone
• Add a small increment (typically 0.5) to handle rounding logic
• Apply `Math.floor` to execute the rounding down
• Divide by the original multiplication factor to restore the decimal shift

Decimal Places

Dealing with decimal places is a common necessity in programming when precision in displayed results is required. Decimal places refer to the number of digits to the right of the decimal point in a number.
In Java, you often manage this using a combination of mathematical operations and functions like `Math.floor`.
For example, if you need to round to the nearest tenth, you manipulate the number so that the tenths place becomes the integer position before applying rounding operations. Consider the number 5.486:

• To round to the nearest tenth (5.5), multiply by 10 to make it 54.86
• Add 0.5, resulting in 55.36
• Use `Math.floor` to get 55
• Divide by 10 to get back to 5.5

This method ensures that your number is rounded correctly according to the specified decimal place.

Java Methods

In Java, methods are blocks of code designed to perform specific tasks. They allow you to encapsulate logic within a reusable unit. In the context of rounding numbers, different methods can be defined to handle rounding to integer and various decimal places.
These methods simplify your main application code by focusing on a single task.
To create a rounding method, you follow these steps:

• Define a method with an appropriate name like `roundToTenths`
• Use parameters to pass numbers that need rounding
• Implement math logic—multiplication, addition, `Math.floor`, and division
• Return the rounded result to be used elsewhere in your program

This modular design improves code clarity and reusability, key principles in software development.

Programming Applications

Rounding is not just a standalone concept; it has practical applications in various programming scenarios. For instance, financial software often requires rounding to two decimal places (cents). Here, rounding functions ensure calculations align with monetary standards.
In scientific programming, numbers might need rounding for precision control, impacting data reporting or computational models.
Consider this simple program structure as an application:

• Read a floating-point number from user's input
• Pass the number to multiple rounding methods
• Display both the original and rounded values

These applications demonstrate how rounding functions integrate with larger systems, providing accuracy while enhancing the readability and robustness of code.