Python 3 - Numbers

Number data types store numeric values. They are immutable data types. This means, changing the value of a number data type results in a newly allocated object.
Number objects are created when you assign a value to them. For example −

var1 = 1
var2 = 10

You can also delete the reference to a number object by using the del statement. The syntax of the del statement is −

del var1[,var2[,var3[....,varN]]]]

You can delete a single object or multiple objects by using the del statement. For example −

del var
del var_a, var_b

Python supports different numerical types −

• int (signed integers) − They are often called just integers or ints. They are positive or negative whole numbers with no decimal point. Integers in Python 3 are of unlimited size. Python 2 has two integer types - int and long. There is no 'long integer' in Python 3 anymore.
• float (floating point real values) − Also called floats, they represent real numbers and are written with a decimal point dividing the integer and the fractional parts. Floats may also be in scientific notation, with E or e indicating the power of 10 (2.5e2 = 2.5 x 10² = 250).
• complex (complex numbers) − are of the form a + bJ, where a and b are floats and J (or j) represents the square root of -1 (which is an imaginary number). The real part of the number is a, and the imaginary part is b. Complex numbers are not used much in Python programming.

It is possible to represent an integer in hexa-decimal or octal form

>>> number = 0xA0F #Hexa-decimal
>>> number
2575

>>> number = 0o37 #Octal
>>> number
31

Examples

Here are some examples of numbers.

int	float	complex
10	0.0	3.14j
100	15.20	45.j
-786	-21.9	9.322e-36j
080	32.3+e18	.876j
-0490	-90.	-.6545+0J
-0×260	-32.54e100	3e+26J
0×69	70.2-E12	4.53e-7j

A complex number consists of an ordered pair of real floating-point numbers denoted by a + bj, where a is the real part and b is the imaginary part of the complex number.

Number Type Conversion

Python converts numbers internally in an expression containing mixed types to a common type for evaluation. Sometimes, you need to coerce a number explicitly from one type to another to satisfy the requirements of an operator or function parameter.

• Type int(x) to convert x to a plain integer.
• Type long(x) to convert x to a long integer.
• Type float(x) to convert x to a floating-point number.
• Type complex(x) to convert x to a complex number with real part x and imaginary part zero.
• Type complex(x, y) to convert x and y to a complex number with real part x and imaginary part y. x and y are numeric expressions

Mathematical Functions

Python includes the following functions that perform mathematical calculations.

S.No.	Function & Returns ( Description )
1	abs(x) The absolute value of x: the (positive) distance between x and zero.
2	ceil(x) The ceiling of x: the smallest integer not less than x.
3	cmp(x, y) -1 if x < y, 0 if x == y, or 1 if x > y. Deprecated in Python 3. Instead use return (x>y)-(x<y).
4	exp(x) The exponential of x: ex
5	fabs(x) The absolute value of x.
6	floor(x) The floor of x: the largest integer not greater than x.
7	log(x) The natural logarithm of x, for x > 0.
8	log10(x) The base-10 logarithm of x for x > 0.
9	max(x1, x2,...) The largest of its arguments: the value closest to positive infinity
10	min(x1, x2,...) The smallest of its arguments: the value closest to negative infinity.
11	modf(x) The fractional and integer parts of x in a two-item tuple. Both parts have the same sign as x. The integer part is returned as a float.
12	pow(x, y) The value of x**y.
13	round(x [,n]) x rounded to n digits from the decimal point. Python rounds away from zero as a tie-breaker: round(0.5) is 1.0 and round(-0.5) is -1.0.
14	sqrt(x) The square root of x for x > 0.

Random Number Functions

Random numbers are used for games, simulations, testing, security, and privacy applications. Python includes the following functions that are commonly used.

S.No.	Function & Description
1	choice(seq) A random item from a list, tuple, or string.
2	randrange ([start,] stop [,step]) A randomly selected element from range(start, stop, step).
3	random() A random float r, such that 0 is less than or equal to r and r is less than 1
4	seed([x]) Sets the integer starting value used in generating random numbers. Call this function before calling any other random module function. Returns None.
5	shuffle(lst) Randomizes the items of a list in place. Returns None.
6	uniform(x, y) A random float r, such that x is less than or equal to r and r is less than y.

Trigonometric Functions

Python includes the following functions that perform trigonometric calculations.

S.No.	Function & Description
1	acos(x) Return the arc cosine of x, in radians.
2	asin(x) Return the arc sine of x, in radians.
3	atan(x) Return the arc tangent of x, in radians.
4	atan2(y, x) Return atan(y / x), in radians.
5	cos(x) Return the cosine of x radians.
6	hypot(x, y) Return the Euclidean norm, sqrt(x*x + y*y).
7	sin(x) Return the sine of x radians.
8	tan(x) Return the tangent of x radians.
9	degrees(x) Converts angle x from radians to degrees.
10	radians(x) Converts angle x from degrees to radians.

Mathematical Constants

The module also defines two mathematical constants −

S.No.	Constants & Description
1	pi The mathematical constant pi.
2	e The mathematical constant e.