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

DECIMALS.
ART. 1. As the local value of figures in the denary scale of notation
increases tenfold reckoned from the right towards the left, the first place
being the place of units, the second the place of tens, the third the
place of hundreds, the fourth the place of thousands, and so on: it
follows that each successive figure decreases tenfold when reckoned
from the left towards the right.
If the scale be continued towards the right and reckoned from the
first place of units, the second, third, fourth, &c., places will be the
places of tenths, hundredths, thousandths, &c. And if a point be
placed before the figure in the place of tenths, this mark will distinguish the fractional from the integral portion of the scale; and while
the integral places successively increase by tens, hundreds, thousands,
%&c., the fractional places successively decrease by tenths, hundredths,
thousandths, &c., from the unit's place.
This extension of the numerical scale reckoning tenfold decrease
towards the right constitutes the perfection of the denary system of
notation, and renders it complete for expressing the smallest possible
fraction as well as the largest possible number.
And further, as these fractions consist only of an extension of the
scale below the place of units to tenths, hundredths, thousandths, and
so on, the operations of addition, subtraction, multiplication, and
division can be performed with these fractions in the same manner as
integers, taking care to mark the values of the results by correctly
placing the point which separates the fractions from the integers.
2. DEF. A decimal fraction or decimal, may be defined to be a
fraction the denominator of which is 10, 100, 1000, &c.
There is a peculiar notation asssumed for expressing these fractions.
The denominators are omitted, and the numerators only are written
with a point placed before that figure, which stands as many places
from the right-hand figure as there are ciphers in the denominator.
If the number of figures in the numerator be less than the number of
ciphers in the denominator, the required number of figures must be
made up by prefixing ciphers to the significant figures of the numerator, in order that each figure of the numerator may occupy its
proper place in the scale.'

1 In order to avoid ambiguity, the point should be placed before the upper
part of the first figure of the decimal, and not before the lower part, as a point
placed between numbers or symbols in the lower part has been assumed, instead
of the symbol X, to denote that the numbers or symbols are multiplied together.