Remainder

Definition and stakes

Portrait of Augustus De Morgan Augustus De Morgan,  Elements of arithmetic (1858)

“ V. Multiply the first divisor by the second figure of the root; if the product be greater than the first dividend, use a lower number for the second figure of the root, and for the last figure of the divisor, until the multiplication just mentioned gives the product less than the first dividend; subtract this from the first dividend, which gives the second remainder. ”
Source: Gutenberg

Portrait of Augustus De Morgan Augustus De Morgan,  Elements of arithmetic (1858)

“ Throwing away the decimal points, then divide 6717300 by 014 or 14 in the usual way, which gives the quotient 479807 and the remainder 2. Hence 479·807 is the answer.
The common rule is: Let the quotient contain as many decimal places as there are decimal places in the dividend more than in the divisor. But this rule becomes inoperative except when there are more decimals in the dividend than in the divisor, and a number of ciphers must be annexed to the former. The rule in the text amounts to the same thing, and provides for an assigned number of decimal places.
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Source: Gutenberg

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