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

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Or, the given repeating decimals may be converted into ordinary
fractions, and the sum or difference of the fractions found, and then
the result may be converted into a decimal if required.
16. PRor. To multiply and divide repeating decimals.
To multiply or divide one repeating decimal by another, or a terminating decimal by a repeating decimal, is a tedious process. In general
it will be found more convenient to reduce the repeating decimals to
ordinary fractions, and find the product or quotient of the fractions,
and afterwards, if necessary, to convert the fractional product or
quotient to its equivalent decimal.1
17. PRor. To find the the au the decimal of any concrete quantity in
s.maller units of the same kind: and conversely, to reduce any concrete
quzantity or decimal to the decimal of any other unit of the same kind.
Concrete decimals are subject to the same rules of operation as
ordinary concrete fractions.
A concrete decimal of a larger unit is reduced to a number or
decimal of a smaller unit of the same kind by multiplying the given
decimal by the number of smaller units contained in the larger.
And, conversely, a concrete number, or decimal of a smaller unit,
is changed into the decimal of a larger unit of the same kind, by
dividing by as many of the smaller units as make one of the greater.
If any of the given decimals be repeating decimals, it will be found
more convenient to change them into ordinary fractions, and employ
them instead of the repeating decimals.2
18. POor. To find the suml or difference of two concrete decimals of the
m.ame kind.
1 Example.-MIultiply and divide 2'27 by 416.
Here 2.27 227 - 2 3 25
99 11 11'
and 4.16 = 4 4 - - 25.
90 6 6
Then 2 27 x 4116 = 5 x 2 = - = 9'469, the product,
11 6 66
and 227 - 416 25 x = 54, the qotient
11 25 11
It may be remarked that sometimes it will be found that the product or quotient
of two repeating decimals may produce a terminating decimal.
2 Example.-What is the value of ~-828125 in units of lower denomination?
The decimal of a pound is reduced to shillings by multiplying by 20, and 6 decimal
places marked off in the product gives 16 shillings.
Next, the decimal of a shilling is reduced to pence by multiplying by 12, and
6 decimals marked off gives the pence 6.
And lastly, the decimal of a penny is reduced to farthings by multiplying by 4,
and 6 places marked off give the farthings 3.
The process may be thus shown: