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If necessary, simplify the long division problem by moving the decimals of the divisor and dividend by the same number of decimal places, to the right (or to the left), so that the decimal of the divisor is to the right of the last digit. When doing long division, keep the numbers lined up straight from top to bottom under the tableau.
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.
Python: the built-in int (3.x) / long (2.x) integer type is of arbitrary precision. The Decimal class in the standard library module decimal has user definable precision and limited mathematical operations (exponentiation, square root, etc. but no trigonometric functions). The Fraction class in the module fractions implements rational numbers ...
Modern calculators and computers compute division either by methods similar to long division, or by faster methods; see Division algorithm. In modular arithmetic (modulo a prime number) and for real numbers, nonzero numbers have a multiplicative inverse. In these cases, a division by x may be computed as the product by the multiplicative ...
Write the original number in decimal form. The numbers are written similar to the long division algorithm, and, as in long division, the root will be written on the line above. Now separate the digits into pairs, starting from the decimal point and going both left and right. The decimal point of the root will be above the decimal point of the ...
The 1620 was a decimal-digit machine which used discrete transistors, yet it had hardware (that used lookup tables) to perform integer arithmetic on digit strings of a length that could be from two to whatever memory was available. For floating-point arithmetic, the mantissa was restricted to a hundred digits or fewer, and the exponent was ...
The pocket-sized Hewlett-Packard HP-35 scientific calculator was the first handheld device of its type, but it cost US$395 in 1972. This was justifiable for some engineering professionals, but too expensive for most students. Around 1974, lower-cost handheld electronic scientific calculators started to make slide rules largely obsolete.
For instance, the rational numbers , , and are written as 0.1, 3.71, and 0.0044 in the decimal fraction notation. [100] Modified versions of integer calculation methods like addition with carry and long multiplication can be applied to calculations with decimal fractions. [ 101 ]