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  2. Simple continued fraction - Wikipedia

    en.wikipedia.org/wiki/Simple_continued_fraction

    The continued fraction representation for a real number is finite if and only if it is a rational number. In contrast, the decimal representation of a rational number may be finite, for example ⁠ 137 / 1600 ⁠ = 0.085625, or infinite with a repeating cycle, for example ⁠ 4 / 27 ⁠ = 0.148148148148...

  3. List of number theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_number_theory_topics

    Unit fraction; Irreducible fraction = in lowest terms; Dyadic fraction; Recurring decimal; Cyclic number; Farey sequence. Ford circle; Stern–Brocot tree; Dedekind sum;

  4. Fixed-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Fixed-point_arithmetic

    A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...

  5. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...

  6. Binary number - Wikipedia

    en.wikipedia.org/wiki/Binary_number

    This is also a repeating binary fraction 0.0 0011... . It may come as a surprise that terminating decimal fractions can have repeating expansions in binary. It is for this reason that many are surprised to discover that 1/10 + ... + 1/10 (addition of 10 numbers) differs from 1 in binary floating point arithmetic. In fact, the only binary ...

  7. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.

  8. Extended precision - Wikipedia

    en.wikipedia.org/wiki/Extended_precision

    Thus, a value such as 10.15, is represented in binary as equivalent to 10.1499996185 etc. in decimal for REAL*4 but 10.15000000000000035527 etc. in REAL*8: inter-conversion will involve approximation, except for those few decimal fractions that represent an exact binary value, such as 0.625 .

  9. Pound sterling - Wikipedia

    en.wikipedia.org/wiki/Pound_sterling

    The Hatter's hat shows an example of the old pre-decimal notation: the hat costs 10/6 (ten shillings and sixpence, a half guinea). Before decimalisation in 1971 , the pound was divided into 20 shillings , and each shilling into 12 pence , making 240 pence to the pound.