Question

Writc a program that reads in two floating-point numbers and tests whether they are the same up to two decimal places. Here are two sample runs. Enter a floating-point nunber; \(2.0\) Enter a floating-point nurber; \(1.99998\) They are the sare up to two decimal places. Enter a floating-point nunber: \(2.0\) Enter a floating-point nunber: \(1.98999\) They are different.

Short answer

Compare numbers rounded to two decimal places to determine if they are the same or different.

Step-by-step solution

Input Two Floating-Point Numbers

Prompt the user to enter the first and second floating-point numbers. Store these inputs in variables, say, `number1` and `number2`, ensuring the inputs are converted from strings to floats.

Convert Numbers to Two Decimal Places

Round `number1` and `number2` to two decimal places. This can be done using the `round()` function in many programming languages, e.g., `round(number1, 2)` and `round(number2, 2)`. This procedure ensures that we check the precision only up to two decimal places.

Compare the Rounded Values

Compare the rounded values of `number1` and `number2`. Utilize an if-else statement to check if the two rounded numbers are equal.

Print the Result

Based on the comparison, print the appropriate message to the user. If the numbers are identical up to two decimal places, print "They are the same up to two decimal places." Otherwise, print "They are different."

Key concepts

Floating-Point Numbers

In Python programming, floating-point numbers are numbers that have decimal points. They are used to represent both whole and fractional parts. This is in contrast to integers, which are whole numbers without any fractional component. Floating-point numbers are particularly important in scientific calculations and when precision is needed.
For instance, numbers like 3.14, 0.001, and -42.56 are all floating-point numbers. When using floating-point numbers, it's crucial to understand their limitations due to the way computers store them. Floating-point arithmetic can introduce tiny rounding errors, which are usually insignificant but may become important in precise calculations.

Decimal Places

When dealing with floating-point numbers, you often need to consider the number of decimal places, which are the number of digits to the right of the decimal point. Rounding floating-point numbers to a certain number of decimal places is crucial for precision control.
The `round()` function in Python is commonly used to round a number to a defined number of decimal places. For example, `round(3.14159, 2)` will result in 3.14. This function helps ensure that calculations are not affected by insignificant tiny differences in floating-point numbers.

• Three decimal places: Example - 2.456
• Two decimal places: Example - 2.46
• One decimal place: Example - 2.5

Understanding how to round numbers properly is essential when accuracy is a priority, such as when comparing two floating-point numbers up to a specific number of decimal places.

Input and Output

In Python, input and output operations allow you to interact with users, collecting data from them and displaying results. To read user input, the `input()` function is used. This function returns the input as a string, so it's often converted to another data type for further processing.
For example, if you need to collect floating-point numbers from a user, you can convert the input string to a float using `float()`, like this: `number = float(input('Enter a number: '))`. This prepares the data for computational operations. After processing this input, output can be produced using the `print()` function, which displays results back to the user. Properly handling input and output makes programs more user-friendly and interactive.

Conditional Statements

Conditional statements in programming, like the `if...else` statemen in Python, allow you to execute certain pieces of code based on specific conditions. They are essential for making decisions within a program. For example, when comparing two numbers to see if they are equal to two decimal places, an `if...else` statement can help determine the outcome.
Here’s a simple example:

• Check if `number1` is equal to `number2` after rounding: `if round(number1, 2) == round(number2, 2):`
• If true, print they are the same: `print("They are the same up to two decimal places.")`
• If false, print they are different: `else: print("They are different.")`

By using conditional statements, you can guide the program's flow, making decisions based on various conditions and yielding useful results.