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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. Extended precision - Wikipedia

    en.wikipedia.org/wiki/Extended_precision

    The use of decimal when talking about binary is unfortunate because most decimal fractions are recurring sequences in binary just as ⁠ 2 / 3 ⁠ is in decimal. 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 ...

  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. 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 ...

  6. Repdigit - Wikipedia

    en.wikipedia.org/wiki/Repdigit

    For a repdigit to be prime, it must be a repunit (i.e. the repeating digit is 1) and have a prime number of digits in its base (except trivial single-digit numbers), since, for example, the repdigit 77777 is divisible by 7, in any base > 7.

  7. 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 ...

  8. Octal - Wikipedia

    en.wikipedia.org/wiki/Octal

    Octal (base 8) is a numeral system with eight as the base.. In the decimal system, each place is a power of ten.For example: = + In the octal system, each place is a power of eight.

  9. Pound sterling - Wikipedia

    en.wikipedia.org/wiki/Pound_sterling

    The value of the index in 1751 was 5.1, increasing to a peak of 16.3 in 1813 before declining very soon after the end of the Napoleonic Wars to around 10.0 and remaining in the range 8.5–10.0 at the end of the 19th century. The index was 9.8 in 1914 and peaked at 25.3 in 1920, before declining to 15.8 in 1933 and 1934—prices were only about ...