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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or ⁠ ⁠, where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include ⁠ 1 2 ⁠, − ⁠ 8 5 ⁠, ⁠ −8 5 ⁠, and ⁠ 8 −5 ⁠.

  3. Continued fraction (generalized) - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction...

    Lagrange's discovery implies that the canonical continued fraction expansion of the square root of every non-square integer is periodic and that, if the period is of length p > 1, it contains a palindromic string of length p − 1. In 1813 Gauss derived from complex-valued hypergeometric functions what is now called Gauss's continued fractions ...

  4. Unit fraction - Wikipedia

    en.wikipedia.org/wiki/Unit_fraction

    Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n. It is the multiplicative inverse (reciprocal) ...

  5. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    Fractions such as ⁠ 22 / 7 ⁠ and ⁠ 355 / 113 ⁠ are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value. [21] Because π is irrational, it has an infinite number of digits in its decimal representation , and does not settle into an infinitely repeating pattern of digits.

  6. Division (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Division_(mathematics)

    Sometimes this remainder is added to the quotient as a fractional part, so 10 / 3 is equal to ⁠3 + 1 / 3 ⁠ or 3.33..., but in the context of integer division, where numbers have no fractional part, the remainder is kept separately (or exceptionally, discarded or rounded). [5] When the remainder is kept as a fraction, it leads to a rational ...

  7. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    Conversely the period of the repeating decimal of a fraction ⁠ c / d ⁠ will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction ⁠ 2 / 7 ⁠ has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction ⁠ 2 / 7 ⁠ is ...

  8. Ratio - Wikipedia

    en.wikipedia.org/wiki/Ratio

    Ratio. In mathematics, a ratio (/ ˈreɪʃ (i) oʊ /) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and ...

  9. Decimal - Wikipedia

    en.wikipedia.org/wiki/Decimal

    An example of a fraction that cannot be represented by a decimal expression (with a finite number of digits) is ⁠ 1 / 3 ⁠, 3 not being a power of 10. More generally, a decimal with n digits after the separator (a point or comma) represents the fraction with denominator 10 n, whose numerator is the integer obtained by removing the separator.

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