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  2. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number ⁠ 5 / 74 ⁠: 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.

  3. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    For example, ⁠ ⁠ is a rational number, as is every integer (for example, =). The set of all rational numbers, also referred to as " the rationals ", [ 2 ] the field of rationals [ 3 ] or the field of rational numbers is usually denoted by boldface Q , or blackboard bold ⁠ Q . {\displaystyle \mathbb {Q} .}

  4. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    Not all rational numbers have a finite representation in the decimal notation. For example, the rational number corresponds to 0.333... with an infinite number of 3s. The shortened notation for this type of repeating decimal is 0. 3. [102] Every repeating decimal expresses a rational number. [103]

  5. Binary number - Wikipedia

    en.wikipedia.org/wiki/Binary_number

    The base-2 numeral system is a positional notation with a radix of 2.Each digit is referred to as a bit, or binary digit.Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because ...

  6. Integer - Wikipedia

    en.wikipedia.org/wiki/Integer

    The integers arranged on a number line. An integer is the number zero , a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). [1] The negations or additive inverses of the positive natural numbers are referred to as negative integers. [2]

  7. Irrational number - Wikipedia

    en.wikipedia.org/wiki/Irrational_number

    Examples are e r and π r, which are transcendental for all nonzero rational r. Because the algebraic numbers form a subfield of the real numbers, many irrational real numbers can be constructed by combining transcendental and algebraic numbers. For example, 3 π + 2, π + √ 2 and e √ 3 are irrational (and even transcendental).

  8. Natural number - Wikipedia

    en.wikipedia.org/wiki/Natural_number

    For example, the integers are made by adding 0 and negative numbers. The rational numbers add fractions, and the real numbers add infinite decimals. Complex numbers add the square root of −1. This chain of extensions canonically embeds the natural numbers in the other number systems. [6] [7] Natural numbers are studied in different areas of math.

  9. 0.999... - Wikipedia

    en.wikipedia.org/wiki/0.999...

    This is true of the binary expansions of many rational numbers, where the values of the numbers are equal but the corresponding binary tree paths are different. For example, 0.10111... 2 = 0.11000... 2 , which are both equal to ⁠ 3 4 {\displaystyle \textstyle {\frac {3}{4}}} ⁠ , but the first representation corresponds to the binary tree ...