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  2. Napier's bones - Wikipedia

    en.wikipedia.org/wiki/Napier's_bones

    Single-digit numbers are written in the bottom right triangle leaving the other triangle blank, while double-digit numbers are written with a digit on either side of the diagonal. If the tables are held on single-sided rods, 40 rods are needed in order to multiply 4-digit numbers – since numbers may have repeated digits, four copies of the ...

  3. Lattice multiplication - Wikipedia

    en.wikipedia.org/wiki/Lattice_multiplication

    As an example, consider the multiplication of 58 with 213. After writing the multiplicands on the sides, consider each cell, beginning with the top left cell. In this case, the column digit is 5 and the row digit is 2. Write their product, 10, in the cell, with the digit 1 above the diagonal and the digit 0 below the diagonal (see picture for ...

  4. Trachtenberg system - Wikipedia

    en.wikipedia.org/wiki/Trachtenberg_system

    Trachtenberg system. The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian engineer Jakow Trachtenberg in order to keep his mind occupied while being in a Nazi concentration ...

  5. Mental calculation - Wikipedia

    en.wikipedia.org/wiki/Mental_calculation

    Another method is to simply multiply the number by 10, and add the original number to the result. For example: 17 × 11 17 × 10 = 170 170 + 17 = 187 17 × 11 = 187 One last easy way: If one has a two-digit number, take it and add the two numbers together and put that sum in the middle, and one can get the answer.

  6. Order of magnitude - Wikipedia

    en.wikipedia.org/wiki/Order_of_magnitude

    An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. To round a number to its nearest order of magnitude, one ...

  7. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [ 1][ 2][ 3] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most single-digit ...

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