Elementary arithmetic, with brief notices of its history... by Robert Potts.

4
~Case 1. When the number of decimals in the dividend is greater
than the number in the divisor:Let 73-77238 be divided by 3-457.
2731772380457
Here 73'77238 = 3778 and 3457 3457
=100000 'ad347- 1000
7377238 3457
Then 77'77238 457 = 77728. 3457
100000 ~ 1000
7377238 1000
100000 x5457
= 21 3, a decimal of two places,
= 21-34.
Hence, when the number of decimals in the dividend is greater than
the number in the divisor, the number in the quotient will be equal
to the excess of the number in the dividend above that in the divisor.
Case 2. When the number of decimals in the dividend is equal to
the number in the divisorLet 7377*238 be divided by 3-457.
7377238 3457
Here 7377.238 =, and 3.457 =
1000 1000'
Then 7377'238 - 3.457 7377238. 3457
1000 1000
7377238 1000
1000 3457
7377238
3457
= 2134 an integer.
Hence, when the number of decimals in the dividend is equal to the
number in the divisor, the quotient will be an integer.
Case 3. When the number of decimals in the dividend is less than
the number in the divisor.
Let 737723-8 be divided by -3457.
Here 73772388 = 7 and.3457 = 7
10 10000
greater than, equal to, or less than the number of decimals in a divisor. Hence
there will arise three cases in division of decimals to be considered.
Abbreviated methods have been devised both for the multiplication and division
of decimals, whereby the number of figures employed in these operations may be
somewhat lessened; and these methods were doubtless very useful in operations
requiring a large number of figures. But since the invention of logarithms, these
abbreviated methods are of no great practical utility, as such operations can be
easily effected by the use of logarithmic tables.