Examples for

# Numbers

Numbers are mathematical entities that originally came into use to satisfy a need to count objects and measure quantities. From tallying systems and counting numbers to integers, zero, rational numbers, irrational numbers, complex numbers and beyond, progressively broader sets of numbers came into use over time as the need for more general numeric entities arose. Use Wolfram|Alpha's computational knowledge of these and other number sets and systems to identify their properties or to perform calculations in and across their respective domains.

Perform arithmetic with integers or compute properties about a particular integer.

#### Compute properties of an integer:

#### Do exact arithmetic with integers:

#### Compute a prime factorization:

Perform computations with or identify the properties of numbers that cannot be expressed as quotients of integers.

#### Compute properties of an irrational number:

#### Determine whether a number is irrational:

Work with the set of numbers with real and imaginary parts.

#### Do basic arithmetic on complex numbers:

#### Find roots of complex numbers:

#### Apply functions to complex numbers:

Attempt to express approximate numbers using exact numbers, and vice versa.

#### Find possible closed forms for an approximate number:

#### Represent an approximate number in terms of specified constants:

Find a number name, determine properties of a named number or solve word problems containing named numbers.

#### Find the English name of a large number:

#### Specify a number by name:

Perform computations with or identify the properties of numbers that can be expressed as quotients of integers.

#### Compute properties of a rational number:

#### Compute the exact value of a repeating decimal:

Check whether numbers are algebraic, compute the properties of algebraic numbers or find minimal polynomials of algebraic numbers.

#### Determine whether a number is algebraic:

#### Identify algebraic integers and units:

Perform computations without sacrificing accuracy.

#### Do exact arithmetic with large numbers:

#### Find a decimal approximation:

#### Compute a decimal approximation to a specified number of digits:

Convert numbers to and from different number bases and compute the results of a variety of bitwise, arithmetic and other operations in non-decimal number bases.

#### Convert a decimal number to another base:

#### Convert a number in a given base to decimal:

#### Do mixed-base computations:

Find the most specific number type that encompasses all possible outputs from an expression involving general number types.

#### Determine parity:

#### Determine sign:

#### Determine number type:

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Ask about nonalgebraic numbers.

#### Determine whether a number is transcendental:

#### Get information about a transcendental number:

Learn about and utilize well-known constants from different areas of mathematics.

#### Compute the value of a mathematical constant:

#### Do computations involving constants:

Convert numbers to and from historical number systems.