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

11
The value of each of the concrete decimals may be found in smaller
units of the same kind, and then their sum or difference.
Or if the given decimals be of different units, they may be reduced to
equivalent decimals of the same unit, and the sum or difference can be
found as in abstract decimals.
If, however, any of the decimals be repeating decimals, these may,
with greater convenience, be reduced to their equivalent ordinary
fractions before performing the operations.
19. PROP. To fnd the product or quotient of two concrete decimals.
If the given decimals be terminating decimals, the product or
quotient can be found in the same way as if the decimals were abstractIf one or both of them be repeating decimals, it will be found necessary in all cases of multiplication or division, first to reduce the given
repeating decimals to their equivalent ordinary fractions, and then
to perform the operation required.
If one of the given decimals be concrete and the other abstract, orif both be concrete, the nature of the product or quotient will be determined by the same considerations as the product or quotient of two
concrete integers or ordinary fractions.
~*828125
20
s. 16'562500
12
d. 6'750000
4
q. 3'000000 so that ~'828125 = 16s. 62d.
Conversely.-To express 16s. 61d. as the decimal of one pound.
First: 3 farthings with ciphers annexed as decimals, divided by 4, gives the
decimal -75 of 1 penny.
Next: 6'75d, with ciphers annexed as decimals, divided by 12, gives '5625 of
1 shilling
And 16'5625s., with ciphers annexed, divided by 20, gives -828125 of 1 pcund.
The process may be exhibited thus:4)3-00
12)6-7500d.
20)16 562500s.
~'828125
In all other concrete quantities which according to their nature are divisible
into larger and smaller units, by a similar method may be found the units of a
smaller unit in any decimal of a larger unit; and conversely, any smaller units maybe reduced to the decimal of any larger unit of the same kind.
Example. —What is the exact value of ~-516 sterling?
516 - 51 465 31
Here ~'516 = -516 of ~1 - -of ~1.
900 900 - 60
And 31 of ~1 = = 0 = 21 of Is. = 10s. 4d.
60 60 1 3