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. 
Example: If we want to round off a number, say 3.5. It will be rounded to the nearest whole number which is 4. However, the number 3.74 will be rounded to one decimal place to give 3.7. 

Method 1: Using Built-in round() Function.
In Python there is a built-in round() function which 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 are not provided for rounding off, the function rounds off the given number n to the nearest integer. 

Syntax: round(number, number of digits)

Parameters: 

  • number: The number to be rounded
  • number of digits (Optional): The number of digits up to which the given number is to be rounded

Example: 



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# For integers
print(round(11))
  
# For floating point
print(round(22.7))  
  
# if the second parameter is present
  
# when the (ndigit+1)th digit is =5 
print(round(4.465, 2)) 
    
# when the (ndigit+1)th digit is >=5 
print(round(4.476, 2))   
    
# when the (ndigit+1)th digit is <5 
print(round(4.473, 2))

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Output: 

11
23
4.46
4.48
4.47

Method 2: Using Truncation concept.
Truncation is one of the simplest methods to round a number which involves truncating a number to a given number of digits. In this function, each digit after a given position is replaced with 0. truncate() function can be used with positive as well as negative numbers. 

Truncation function can be implemented in following way:

  • Multiplying the number by 10^p (10 raised to the pth 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.

Implementation of the Truncation concept using truncate() user-defined function: 

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# defining truncate function
# second argument defaults to 0
# so that if no argument is passed 
# it returns the integer part of number
  
def truncate(n, decimals = 0):
    multiplier = 10 ** decimals
    return int(n * multiplier) / multiplier
  
print(truncate(16.5))
print(truncate(-3.853, 1))
print(truncate(3.815, 2))
  
# we can truncate digits towards the left of the decimal point
# by passing a negative number.
print(truncate(346.8, -1))
print(truncate(-2947.48, -3))

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Output: 

16.0
-3.8
3.81
340.0
-2000.0

Method 3: 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. 
Example:

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# import math library
import math
  
# ceil value for positive
# decimal number
print(math.ceil(4.2))
  
# ceil value for negative
# decimal number
print(math.ceil(-0.5))
  
# floor value for decimal 
# and negative number
print(math.floor(2.2))
print(math.floor(-0.5))

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Output: 

5
0
2
-1

Method 3: Using Rounding Up concept.
In Rounding Up a number is rounded up to a specified number of digits. 
 



Rounding up function can be implemented in following way: 

  • First the decimal point in n is shifted 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.

Implementation of the rounding up concept using round_up() user-defined function:

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# import math library
import math
  
# define a function for 
# round_up
def round_up(n, decimals = 0): 
    multiplier = 10 ** decimals 
    return math.ceil(n * multiplier) / multiplier
  
# passing positive values
print(round_up(2.1))
print(round_up(2.23, 1))
print(round_up(2.543, 2))
  
# passing negative values
print(round_up(22.45, -1))
print(round_up(2352, -2))

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Output: 

3.0
2.3
2.55
30.0
2400.0

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

Understanding Rounding Up and Rounding Down

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. 
Method 5: Using Rounding Down concept.

In Rounding Down a number is rounded down to a specified number of digits. 

Rounding down function can be implemented in following way: 

  • First the decimal point in n is shifted 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.

Implementation of the rounding down concept using round_down() user-defined function:

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import math
  
# defining a function for
# round down.
def round_down(n, decimals=0):
    multiplier = 10 ** decimals
    return math.floor(n * multiplier) / multiplier
  
# passing different values to function
print(round_down(2.5))
print(round_down(2.48, 1))
print(round_down(-0.5))

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Output: 



2.0
2.4
-1.0

Method 5: Using Rounding Bias concept.
The concept of symmetry introduces the notion of rounding bias, that 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 behaviour are said to have a round towards zero bias, in general. 

a) Rounding Half Up concept.
The rounding half up rounds every number to the nearest number with the specified precision and breaks ties by rounding up. 
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: 

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import math
  
# defining round_half_up
  
def round_half_up(n, decimals=0):
    multiplier = 10 ** decimals
    return math.floor(n * multiplier + 0.5) / multiplier
  
# passing different values to the function
  
print(round_half_up(1.28, 1))
print(round_half_up(-1.5))
print(round_half_up(-1.225, 2))

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Output: 

1.3
-1.0
-1.23

b) Rounding Half Down concept.
This rounds to the nearest number similarly like rounding half up method, the difference is that it breaks ties by rounding to the lesser of the two numbers. Rounding half down strategy is implemented by replacing math.floor() in the round_half_up() function with math.ceil() and then by subtracting 0.5 instead of adding. 

Implementation of round_half_down() function: 

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# import math library
import math
  
# defining a function
# for round_half_down
def round_half_down(n, decimals=0):
    multiplier = 10 ** decimals
    return math.ceil(n * multiplier - 0.5) / multiplier
  
# passing different values to the function
print(round_half_down(2.5))
print(round_half_down(-2.5))
print(round_half_down(2.25, 1))

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Output: 

2.0
-3.0
2.2

Method 6: Rounding Half Away From Zero.
In Rounding Half Away From Zero we need to do is to start as usual by shifting the decimal point to the right a given number of places and then notice the digit(d) immediately to the right of the decimal place in the new number. There are four cases to consider:

  • If n is positive and d >= 5, round up
  • If n is positive and d = 5, round down
  • If n is negative and d >= 5, round down
  • If n is negative and d < 5, round up

After rounding as per the rules mentioned above, we can shift the decimal place back to the left. 

  • Rounding Half To Even: There is a way to mitigate rounding bias while we are rounding values in a dataset. We can simply round ties to the nearest even number at the desired precision. The rounding half to even strategy is the strategy used by Python’s built-in round(). The decimal class provides support for fast correctly-rounded decimal floating-point arithmetic. This offers several advantages over the float datatype. The default rounding strategy in the decimal module is ROUND_HALF_EVEN.

Example: 

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# import Decimal function from 
# decimal library
from decimal import Decimal
print(Decimal("0.1"))
print(Decimal(0.1))
  
# Rounding a Decimal number is
# done with the .quantize() function
# "1.0" in .quantize() determines the
# number of decimal places to round the number
print(Decimal("1.65").quantize(Decimal("1.0")))
print(Decimal("1.675").quantize(Decimal("1.00")))

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Output: 

0.1
0.1000000000000000055511151231257827021181583404541015625
1.6
1.68

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