Editing Napier's bones (section)

== Division ==
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Division is performed in a similar fashion. To divide 46785399 by 96431, the bars for the divisor (96431) are placed on the board, as shown in the graphic below.  Using the [[abacus]], all the products of the divisor from 1 to 9 are found by reading the displayed numbers.  Note that the dividend has eight digits, whereas the partial products (save for the first one) all have six.  So the final two digits of 46785399, namely the '99', are temporarily ignored, leaving the number 467853. Then, the greatest partial product that is less than the truncated dividend is found. In this case, 385724. Two things must be marked down, as seen in the diagram:  since 385724 is in the '4' row of the abacus, a '4' is marked down as the left-most digit of the quotient; the partial product, left-aligned, under the original dividend, is also written. The two terms are subtracted, which leaves 8212999. The same steps are repeated: the number is truncated to six digits, the partial product immediately less than the truncated number is chosen, the row number is written as the next digit of the quotient, and the partial product is subtracted from the difference found in the first repetition. The process is shown in the diagram. The cycle is repeated until the result of subtraction is less than the divisor. The number left is the remainder.

[[Image:Napier-example-3.png|center]]

So in this example, what remains is a quotient of 485 with a remainder of 16364. The process usually stops here and the answer uses the fractional form {{sfrac|485|16364|96431}}.

For more accuracy, the cycle is continued to find as many decimal places required.  A decimal point is marked after the last digit of the quotient and a zero is appended to the remainder which leaves 163640. The cycle is continued, each time appending a zero to the
result after the subtraction.