Python Round Up: Effortlessly Rounding Numbers

How to Round Numbers in Python

With many businesses turning to Python’s powerful data science ecosystem to analyze their data, understanding how to avoid introducing bias into datasets is absolutely vital. If you’ve studied some statistics, then you’re probably familiar with terms like reporting bias, selection bias, and sampling bias. There’s another type of bias that plays an important role when you’re dealing with numeric data: rounding bias.

Understanding how rounding works in Python can help you avoid biasing your dataset. This is an important skill. After all, drawing conclusions from biased data can lead to costly mistakes.

In this tutorial, you’ll learn:

Why the way you round numbers is important
How to round a number according to various rounding strategies
How to implement each strategy in pure Python
How rounding affects data and which rounding strategy minimizes this effect
How to round numbers in NumPy arrays and pandas DataFrames
When to apply different rounding strategies

Take the Quiz: Test your knowledge with our interactive “Rounding Numbers in Python” quiz. Upon completion, you will receive a score so you can track your learning progress over time.

Free Bonus: Click here to download sample code to ensure that your numbers are always well-rounded!

You won’t get a treatise on numeric precision in computing, although you’ll touch briefly on the subject. Only a familiarity with the fundamentals of Python is necessary, and the math should feel familiar if you’ve had high school algebra.

You’ll start by looking at Python’s built-in rounding mechanism.

Python’s Built-in `round()` Function

Python has a built-in round() function that takes two numeric arguments, n and ndigits, and returns the number n rounded to ndigits. The ndigits argument defaults to zero, so leaving it out results in a number rounded to an integer. As you’ll see, round() may not work quite as you expect.

The way most people are taught to round a number goes something like this:

Round the number n to p decimal places by first shifting the decimal point in n by p places. To do that, multiply n by 10^p (10 raised to the p power) to get a new number, m.
Then look at the digit d in the first decimal place of m. If d is less than 5, round m down to the nearest integer. Otherwise, round m up.
Finally, shift the decimal point back p places by dividing m by 10^p.

Now open up an interpreter session and round 2.5 to the nearest whole number using Python’s built-in round() function:

>>> round(2.5)
3

As you can see, round() rounds 2.5 up to 3.

Let’s try rounding 2.4 to the nearest whole number:

>>> round(2.4)
2

In this case, round() rounds 2.4 down to 2.

The behavior of the round() function might seem counterintuitive, especially if you expected it to round decimal values of .5 up. This rounding behavior is known as “round half to even,” or “round half down.” The idea is to round to the nearest even number if the decimal value is .5.

Now let’s explore some other rounding strategies in Python.

Rounding Half Up

To round a number to the nearest whole number, you can use the math.ceil() function from the built-in math module, which always rounds up.

The math.ceil() function takes a single argument, x, and returns the smallest integer that is greater than or equal to x.

Here’s an example:

import math

x = 2.5
rounded = math.ceil(x)

print(rounded)  # Output: 3

In this example, math.ceil(2.5) returns 3, which is the nearest integer greater than or equal to 2.5.

Rounding Half Down

To round a number down to the nearest whole number, you can use the math.floor() function from the math module, which always rounds down.

The math.floor() function takes a single argument, x, and returns the largest integer that is less than or equal to x.

Here’s an example:

import math

x = 2.5
rounded = math.floor(x)

print(rounded)  # Output: 2

In this example, math.floor(2.5) returns 2, which is the nearest integer less than or equal to 2.5.

Rounding Half Away From Zero

The round() function in Python uses another rounding strategy known as “round half away from zero.” This strategy is similar to “round half up,” but it rounds negative values in the opposite direction.

Here’s an example:

x = 2.5
rounded = round(x)

print(rounded)  # Output: 3

In this example, round(2.5) returns 3, which is the nearest integer obtained by rounding 2.5 using the “round half away from zero” strategy.

Rounding Half to Even

The round() function in Python uses the “round half to even” strategy by default. This strategy rounds to the nearest even number if the decimal value is .5.

Here’s an example:

x = 2.5
rounded = round(x)

print(rounded)  # Output: 2

In this example, round(2.5) returns 2, which is the nearest even number obtained by rounding 2.5 using the “round half to even” strategy.

The Decimal Class

Python provides the decimal module, which allows you to perform decimal arithmetic and precision rounding. This module provides the Decimal class, which can be used to create decimal objects with a specified number of decimal places.

Here’s an example:

from decimal import Decimal, ROUND_HALF_UP

x = Decimal('2.5')
rounded = x.quantize(Decimal('1'), ROUND_HALF_UP)

print(rounded)  # Output: 3

In this example, x.quantize(Decimal('1'), ROUND_HALF_UP) rounds x to 1 decimal place using the “round half up” strategy.

The quantize() method of the Decimal class takes two arguments: decimal_places, which specifies the number of decimal places to round to, and rounding, which specifies the rounding strategy. In this case, Decimal('1') specifies 1 decimal place, and ROUND_HALF_UP specifies the “round half up” strategy.

Rounding NumPy Arrays

NumPy is a powerful library for numerical computing in Python. It provides support for working with arrays and matrices of numeric data. NumPy also provides functions for rounding array elements according to various rounding strategies.

Here’s an example of rounding a NumPy array using the “round half up” strategy:

import numpy as np

x = np.array([1.1, 2.2, 3.3, 4.4, 5.5])
rounded = np.round(x)

print(rounded)  # Output: [1. 2. 3. 4. 6.]

In this example, np.round(x) rounds each element of the NumPy array x to the nearest whole number.

NumPy provides several other rounding functions, such as np.ceil() and np.floor(), which round up and down to the nearest whole number, respectively.

Rounding pandas Series and DataFrame

pandas is a powerful data manipulation and analysis library for Python. It provides data structures like Series and DataFrame, which are optimized for efficient data handling and analysis. pandas also provides functions for rounding Series and DataFrame elements according to various rounding strategies.

Here’s an example of rounding a pandas Series using the “round half up” strategy:

import pandas as pd

s = pd.Series([1.1, 2.2, 3.3, 4.4, 5.5])
rounded = s.round()

print(rounded)

In this example, s.round() rounds each element of the pandas Series s to the nearest whole number.

For pandas DataFrames, you can use the applymap() method to apply a rounding function to each element of the DataFrame.

Applications and Best Practices

Rounding numbers is a common task in data analysis and financial applications. Here are a few applications and best practices for rounding numbers in Python:

Store More and Round Late: When working with large datasets or performing complex calculations, it is often a good practice to store raw data with high precision and round the values only when necessary for reporting or analysis purposes.
Obey Local Currency Regulations: When dealing with financial calculations involving currencies, it’s important to round the values according to local currency regulations to ensure accuracy and compliance.
When in Doubt, Round Ties to Even: If you are unsure of the appropriate rounding strategy to use, the “round half to even” strategy is a good choice as it minimizes the overall rounding bias.

Conclusion

In this tutorial, you learned about the various rounding strategies in Python and how to implement them using built-in functions, modules like math and decimal, and libraries like NumPy and pandas. You also explored some applications and best practices for rounding numbers.

Rounding numbers correctly is essential when working with data, especially in statistical analysis and financial applications. By understanding and applying the appropriate rounding strategy, you can ensure the accuracy and integrity of your data.

Now you have the knowledge and tools to round numbers in Python. Start applying these techniques in your data analysis projects to avoid introducing bias and make more accurate conclusions from your data.

Additional Resources

If you’re interested in learning more about Python and data science, check out the following resources:

Let’s round numbers in Python with confidence and accuracy!

Python Round Up: Effortlessly Rounding Numbers

How to Round Numbers in Python

Python’s Built-in round() Function

Rounding Half Up

Rounding Half Down

Rounding Half Away From Zero

Rounding Half to Even

The Decimal Class

Rounding NumPy Arrays

Rounding pandas Series and DataFrame

Applications and Best Practices

Conclusion

Additional Resources

Python’s Built-in `round()` Function