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.

Integers

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:

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Irrational Numbers

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:

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Complex Numbers

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:

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Number Recognition

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:

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Number Names

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:

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Rational Numbers

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:

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Algebraic Numbers

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:

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Arbitrary Precision

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:

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Base Conversions

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:

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Number Type Arithmetic

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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RELATED EXAMPLES

  • Elementary Math
  • Number Lines
  • Number Theory
  • Numerical Analysis
  • Real Intervals
  • RELATED WOLFRAM RESOURCES

  • Wolfram Numbers Overview Page
  • Transcendental Numbers

    Ask about nonalgebraic numbers.

    Determine whether a number is transcendental:

    Get information about a transcendental number:

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    Mathematical Constants

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

    Compute the value of a mathematical constant:

    Do computations involving constants:

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    Historical Numbers

    Convert numbers to and from historical number systems.

    Do computations with Roman numerals:

    Convert a decimal number to Mayan numerals:

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