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  2. Numeric precision in Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Numeric_precision_in...

    Here the 'IEEE 754 double value' resulting of the 15 bit figure is 3.330560653658221E-15, which is rounded by Excel for the 'user interface' to 15 digits 3.33056065365822E-15, and then displayed with 30 decimals digits gets one 'fake zero' added, thus the 'binary' and 'decimal' values in the sample are identical only in display, the values ...

  3. Modular exponentiation - Wikipedia

    en.wikipedia.org/wiki/Modular_exponentiation

    Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m. For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8.

  4. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.

  5. Remainder - Wikipedia

    en.wikipedia.org/wiki/Remainder

    The remainder, as defined above, is called the least positive remainder or simply the remainder. [2] The integer a is either a multiple of d, or lies in the interval between consecutive multiples of d, namely, q⋅d and (q + 1)d (for positive q). In some occasions, it is convenient to carry out the division so that a is as close to an integral ...

  6. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    explicitly showing its relationship with Euclidean division. However, the b here need not be the remainder in the division of a by m. Rather, a ≡ b (mod m) asserts that a and b have the same remainder when divided by m. That is, a = p m + r, b = q m + r, where 0 ≤ r < m is the common remainder.

  7. Division (mathematics) - Wikipedia

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

    The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...

  8. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    Calculate the remainders left by each product on dividing by 7. Add these remainders. The remainder of the sum when divided by 7 is the remainder of the given number when divided by 7. For example: The number 194,536 leaves a remainder of 6 on dividing by 7. The number 510,517,813 leaves a remainder of 1 on dividing by 7.

  9. Division algorithm - Wikipedia

    en.wikipedia.org/wiki/Division_algorithm

    Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.