Round python with zeros

Python Rounding

Summary: in this tutorial, you’ll learn how to use the Python round() function to round a number.

Introduction to the Python round() function

Rounding means making a number simpler but keeping its value close to its original value. For example, 89 rounded to the nearest ten is 90 because 89 is closer to 90 than to 80.

To round a number in Python, you use the built-in round() function:

round(number [, ndigits])Code language: Python (python)

The round() function rounds the number to the closest multiple of 10 -ndigits .

In other words, the round() function returns the number rounded to ndigits precision after the decimal point.

If ndigits is omitted or None , the round() will return the nearest integer.

Python round() function examples

Let’s take some examples to understand the round() function better.

1) Python round() function examples

The following example uses the round() function without passing the ndigits :

round(1.25)Code language: Python (python)

1Code language: Python (python)

However, if you pass ndigits as zero, the round() function returns a float 1.0:

round(1.25, 0)Code language: Python (python)

1.0Code language: Python (python)

The following illustrates how the round() function works under the hood:

Since ndigits is zero, the round() function rounds the number 1.25 to the closet multiple of 10 -(0) = 1.

2) Python round() function example with negative ndigits

The following example uses the round() function with negative ndigits :

round(15.5, -1)Code language: Python (python)

Because ndigits is -1 , the round() function rounds the number 15.5 to the closest multiple of 20 (10 -(-1) ):

Since 15.5 is situated between 10 and 20 (multiple of 10 ), it’s closer to 20 . Therefore, the round() function returns 20 .

3) Python round() function example with ties

When you round a number situated in the middle of two numbers, Python cannot find the closest number.

For example, if you round the number 1.25 with n is 1 . There will be no closest number:

In this case, Python uses the IEEE 754 standard for rounding, called the banker’s rounding.

In the banker’s rounding, a number is rounded to the nearest value, with ties rounded to the nearest value with an even least significant digit.

Generally, the least significant digit in a number is the rightmost digit.

The banker’s rounding comes from the idea that statistically 50% sample of numbers are rounded up and 50% are rounded down.

round(1.25, 1)Code language: Python (python)

Because the least significant digit of 1.2 is 2 , which is even:

Similarly, the rounding of 1.35 will return 1.4 :

round(1.35, 1)Code language: Python (python)

Python uses banker’s rounding but not rounding away from zero because it’s less biased.

For example, if you average three numbers 1.5 , 2.5 , and 3.5 , the rounding away from zero returns 3 .0 while the banker’s rounding returns 2.66 :

Number	Banker’s Rounding	Rounding away from zero
1.5	2	2
2.5	2	3
3.5	4	4
Average	2.66666…	3.0

How to round away from zero

Python doesn’t provide a direct way to round a number away from zero as you might expect. For example:

Number	Rounding away from zero
1.2	1
1.5	2

A common way to round a number away from zero is to use the following expression:

int(x + 0.5)Code language: Python (python)

This expression works correctly for positive numbers. For example:

print(int(1.2 + 0.5)) print(int(1.5 + 0.5))Code language: Python (python)

1 2Code language: Python (python)

However, it doesn’t work for the negative numbers:

print(int(-1.2 + 0.5)) print(int(-1.5 + 0.5))Code language: Python (python)

0 -1Code language: Python (python)

For negative numbers, you should subtract 0.5 instead of adding it.

The following example works properly for the negative numbers:

print(int(-1.2 - 0.5)) print(int(-1.5 - 0.5))Code language: Python (python)

The following defines a helper function that rounds up a number:

def round_up(x): if x > 0: return int(x + 0.5) return int(x - 0.5)Code language: Python (python)

The Python math module provides you with a function called copysign() :

math.copysign(x, y)Code language: Python (python)

The copysign() function returns the absolute value of x but the sign of y .

And you can use this copysign() function to develop a round_up() function without checking whether x is positive or negative:

from math import copysign def round_up(x): return int(x + copysign(0.5, x))Code language: Python (python)

Summary

• Use the round(number, ndigits) function to round a number to the ndigits precision after the decimal point.

Источник

How to Round Numbers in Python?

Rounding a number means making the number simpler by keeping its value intact but closer to the next number. Below are the following points that will cover in this article using Python:

• using Built-in round() Function
• using Truncation concept
• using Math.ceil() and Math.floor() functions
• using math.ceil
• using math.floor
• using Rounding Bias concept
• Rounding Half Away From Zero in Python

Input: 3.5 Output: 4 Explanation: Nearest whole number. Input: 3.74 Output: 3.7 Explanation: Rounded to one decimal place.

Round Numbers in Python using Built-in round() Function

In Python, there is a built-in round() function that rounds off a number to the given number of digits. The function round() accepts two numeric arguments, n, and n digits, and then returns the number n after rounding it to n digits. If the number of digits is not provided for rounding off, the function rounds off the given number n to the nearest integer.

python3

Round Numbers in Python using Truncation concept

In this function, each digit after a given position is replaced with 0. python truncate() function can be used with positive as well as negative numbers. The truncation function can be implemented in the following way:

• Multiplying the number by 10^p (10 raised to the p_th power) to shift the decimal point p places to the right.
• Taking the integer part of that new number using int().
• Shifting the decimal place p places back to the left by dividing by 10^p.

python3

Round Numbers in Python using Math.ceil() and Math.floor() functions

Math.ceil(): This function returns the nearest integer that is greater than or equal to a given number.
Math.floor(): This function returns the nearest integer less than or equal to a given number.

python3

Round Numbers in Python using math.ceil

In Rounding Up a number is rounded up to a specified number of digits. The rounding up function can be implemented in the following way:

• First, the decimal point in n is shifted to the correct number of places to the right by multiplying n by 10 ** decimals.
• The new value is rounded up to the nearest integer using math.ceil()
• Finally, the decimal point is shifted back to the left by dividing by 10 ** decimals.

python3

We can follow the diagram below to understand round up and round down. Round up to the right and down to the left.

Rounding up always rounds a number to the right on the number line and rounding down always rounds a number to the left on the number line.

Round Numbers in Python using math.floor

In Rounding Down a number is rounded down to a specified number of digits. The rounding down function can be implemented in the following way:

• First, the decimal point in n is shifted to the correct number of places to the right by multiplying n by 10 ** decimals.
• The new value is rounded up to the nearest integer using math.floor().
• Finally, the decimal point is shifted back to the left by dividing by 10 ** decimals.

python3

Round Numbers in Python using Rounding Bias concept.

The concept of symmetry introduces the notion of rounding bias, which describes how rounding affects numeric data in a dataset.
The rounding up strategy has a round towards positive infinity bias, as the value is always rounded up in the direction of positive infinity. Similarly, the rounding down strategy has a round towards negative infinity bias. The truncation strategy has a round towards negative infinity bias on positive values and a round towards positive infinity for negative values. Rounding functions with this behavior are said to have a round towards zero bias, in general.

a) Rounding Half Up concept in Python

The rounding half-up rounds every number to the nearest number with the specified precision and breaks ties by rounding up.
The rounding half-up strategy is implemented by shifting the decimal point to the right by the desired number of places. In this case, we will have to determine whether the digit after the shifted decimal point is less than or greater than equal to 5.
We can add 0.5 to the value which is shifted and then round it down with the math.floor() function.

Implementation of round_half_up() function:

Источник