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

5
Then 7377238 - 3457 7377238 457
10 ' 10000
7377238 10000
X x 7
10 3457
7377238 x 1000
3457
7377238000
3457
2134000 an integer.
Hence, when the number of decimals in the dividend is less than the
number in the divisor, a number of ciphers equal to the defect must
be annexed to the dividend, and the quotient will be an integer.
If there be a remainder after all the ciphers of the dividend have
been employed, the division may be continued by annexing other
ciphers, considered as decimals, to the dividend, either until the
division terminate, or until any required number of decimals in the
quotient is obtained.1
8. Pnop. A decimal is divided by 10, 100, 1000, &c., by removing the
<decimal point one, two, three, &c., places farther towards the left of the
given decimal.
For any given decimal expressed as a fraction is divided by 10
100, 1000, &c., by multiplying the denominator of the decimal fraction
by 10, 100, 1000, &c., and thus the decimal fraction, when expressed as
a decimal, will consist of 1, 2, 3, &c., decimal places more than before.
9. PnoP. Tb reduce an ordinary fiaction to a decimal.
If the numerator and denominator of any ordinary fraction be both
multiplied by 10, 100, 1000, &c., and the numerator so increased be
divided by the denominator of the given fraction, the result will be
the equivalent decimal fraction.
In practice, this may be more readily effected by annexing one,
two, three, &c., ciphers, as decimals to the numerator, and dividing
by the denominator of the fraction, the quotient will be the equivalent
decimal, consisting of as many places as there were ciphers annexed
to the numerator.
In the conversion of ordinary fractions into their equivalent
decimals, it will be found that in some cases the process of division
will terminate, and in others it will not terminate. Each class of
decimals will require separate considerations in the converse process.2
1 It will be found sometimes convenient in mathematical operations to change a
multiplier into a divisor, and conversely. For instance, since - = '5, it follows
that to multiply by.5 is the same as to multiply by ~ or divide by 2, and conversely.
And in the same way, to divide by '625 is the same as to multiply by 5.
For examples, in the conversion of 1, a, - to their equivalent decimals, as the
denominators respectively consist of one, two, three factors; one, two, three ciphers