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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

Example:

```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 usingBuilt-inround()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

 `# 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``))`

Output:

```11
23
4.46
4.48
4.47```

### 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 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.

## python3

 `# 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``))`

Output:

```16.0
-3.8
3.81
340.0
-2000.0```

### 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

 `# 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``))`

Output:

```5
0
2
-1```

### 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

 `# 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``))`

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. 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

 `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``))`

Output:

```2.0
2.4
-1.0```

### 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:

## python3

 `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``))`

Output:

```1.3
-1.0
-1.23```

b) Rounding Half Down concept in Python

This rounds to the nearest number similar to the 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:

## python3

 `# 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``))`

Output:

```2.0
-3.0
2.2```

### Rounding Half Away From Zero in Python

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:

## python3

 `# 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"``)))`

Output:

```0.1
0.1000000000000000055511151231257827021181583404541015625
1.6
1.68```

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