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

2
Thus, the decimal fraction - is represented by '5, - -,Y y '05,
T b-o by -005, s-o by -876, -'1 -o- by 5-876.1
3. PIor. The value of any decimal is not altered in value by annexing
one, two, three, tc., ciphers to the right hand of it.
For by annexing 1, 2, 3, &c., ciphers to the right hand of a
-decimal, both the numerator and the suppressed denominator of the
decimal fraction are multiplied by 10, 100, 1000, &c.: and if the
numerator and denominator of a fraction be both multiplied by the
same number, the fraction is both multiplied and divided by that
number, and therefore remains unaltered in value.
Also, if one, two, three, 'c., ciphers be found at the right hand of a
decimal, they may be omitted without altering the value of the decimal.
For by omitting 1, 2, 3, &c., ciphers, both the numerator and the
suppressed denominator of the decimal fraction are divided by 10,
100, 1000, &c.; and when both the numerator and denominator of a
fraction are divided by the same number, its value is unaltered.
4. PROP. To find the sum2 or difference of twlo decimals.
If the decimals be reduced to a common denominator, the sum or
difference may be found as the sum or difference of two ordinary
fractions.
The sum or difference, however, may be found without reducing the
decimal fractions to a common denominator, by arranging the numbers
*under each other: units under units, tenths under tenths, and so on,
and then adding or subtracting as in integers, taking care to place the
decimal point in the sum or difference before the place of tenths.2
1 If the equivalent notations -5 and '5 might be named, the former "a decimal
fraction," and the latter " a decimal," an ambiguity would sometimes be avoided in
speaking of the two forms of the same thing.
A decimal may consist wholly of significant figures, as -875 is a decimal of
three places, consisting of three significant figures; or partly of significant figures,
and partly of figures which are not significant, as '005 is a decimal of three places,
consisting of one significant figure.
Any integer may be expressed in the form2 of a decimal fraction, as 25 may be
put into the forms 5o~, I 2,l ~o~ooo &c.
Any decimal may be exhibited as the sum of as many decimals or decimal frac.
tions as there are significant figures in the given decimal.
The decimal '875 may be exhibited as the sumi of three decimal fractions.
s 8 875 800 + 70 + 5
Thus: '875 = 1000
1000 1000
800 70 5
1000 1000 1000
_ 8 7 5
8 + +
10 100 1000
= 8 + -07 + '005
s Example.-To find the sum and difference of 13-1035 and 7'8105689.
13-1035000 13-1035000
7-8105689 7-8105689
20U9140fb9 sum. 5'2929311 difference.