Propriétés des Nombres

Number Properties

Numbers form the foundation of mathematical understanding. They can be categorized into several types based on their properties and uses. Here's a brief overview of some key number properties:

Integer

An integer is any whole number, positive or negative, including zero. Integers have two unique properties, namely divisibility by zero and the commutativity property. An example of an integer expression includes -8 * |-6| = 48 and -9 * (-4) = 36.

Divisibility by Zero Property

An integer is divisible by zero if its quotient with division by zero is defined and equal to exactly one. For example, 10 ÷ 0 = 0, where 0 is both the dividend and the divisor. This rule holds true for all integers except zero itself.

Commutativity Property

The order of the numbers does not affect the result when multiplying or adding them. For instance, 2 + 3 = 3 + 2 and 5 × 9 = 9 × 5.

Fraction

A fraction is a type of number that can be expressed as a quotient of two integers. Fractions have properties such as commutativity, associativity, and the distributive property. For example, (3/4) * (2/5) = (2/5) * (3/4).

Rational Number

A rational number is any number that can be expressed as the quotient of two integers. Rational numbers include integers, fractions, and the decimal expansions of rational numbers.

Irrational Number

An irrational number is a real number that cannot be expressed as a finite decimal or a fraction. Examples of irrational numbers include √2 and π.

Real Number

A real number is any number that can be expressed as a decimal expansion, a fraction, a terminating or non-terminating repeating decimal, or an integer. Real numbers include integers, fractions, and irrational numbers.

Imaginary Number

An imaginary number is a number that can be expressed in the form a*i, where a is a real number and i is the imaginary unit, which is the square root of -1. Imaginary numbers have properties such as addition, subtraction, multiplication, and division. Examples of imaginary numbers include 3i and -4i.

Complex Number

A complex number is a number that can be expressed in the form a + bi, where a is a real number and b is an imaginary number. Complex numbers have properties such as addition, subtraction, multiplication, and division. Examples of complex numbers include 5 + 2i and -3 + 4i.

0.001

0.001 is a real number that can be expressed as the decimal expansion 0.001 or as the fraction 1/1000. It is also an irrational number because it has an infinite, non-repeating decimal expansion.

0.000000001

0.000000001 is a real number that can be expressed as the decimal expansion 0.000000001 or as the fraction 1/1,000,000,000. It is also an irrational number because it has an infinite, non-repeating decimal expansion.

0.00000000000000001

0.00000000000000001 is a real number that can be expressed as the decimal expansion 0.00000000000000001 or as the fraction 1/1,000,000,000,000,000. It is also an irrational number because it has an infinite, non-repeating decimal expansion.

0.000000000000000000000001

0.000000000000000000000001 is a real number that can be expressed as the decimal expansion 0.000000000000000000000001 or as the fraction 1/1,000,000,000,000,000,000. It is also an irrational number because it has an infinite, non-repeating decimal expansion.

0.0000000000000000000000000000001

0.0000000000000000000000000000001 is a real number that can be expressed as the decimal expansion 0.0000000000000000000000000000001 or as the fraction 1/1,000,000,000,000,000,000,000. It is also an irrational number because it has an infinite, non-repeating decimal expansion.

0.000000000000000000000000000000001

0.000000000000000000000000000000001 is a real number that can be expressed as the decimal expansion 0.000000000000000000000000000000001 or as the fraction 1/1,000,000,000,000,000,000,000,000. It is also an irrational number because it has an infinite, non-repeating decimal expansion.

0.00000000000000000000000000000000001

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