DECIMALS. 
Addition and sul)tvaction of decimals are 
the same as in whole numbers, when the 
places of the same denomination are set 
under one anotlier, as in the following 
examples : 
To 34.25 
Add 3.026 
Sum '37.276 
From 16.5 
Subtract .125 
Rem. 16.375 
In multiplication the work is the same as 
in whole numbers, only in the product ; se- 
parate, witli a point, so many figures to the 
right hand as there are fractional places 
both in the multiplicand and multiplier; 
then all the figures on ithe left hand of the 
point make the whole number, and those on 
the right a decimal fraction. 
It is to be noted, that if there be not so 
many figures in the product, as ought to 
be separated by the preceding rule, tlieo 
place cyphers at the left, to complete tlie 
number, as may be seen in Ex. 5. 
Ex. 1. Mult. 456 Ex. -2. Mult. 45.6 
by 21.3 
by 21.3 
1368 
Product 971.28 
456 
— r 
912 
Product 9712.8 
Ex. 3. Multiply 
456 
by 
0.213 
Product 
97.128 
Ex. 4. Multiply 
45.6 
by 
0.213 
Product 
9.7128 
Ex. 5. Multiply 
0.0456 
by 
0.213 
Product 0.0097128 
In division the work is 
the same as in 
7 J VXV..U 
rate, with a point, so many figures to the 
right hand for a decimal fraction, as there 
are fractional places in the dividend, more 
than in the divisor, because there must be 
so many fractional places in the divisor and 
quotient together, as there are in the divi- 
dend. 
As division of decimal fractions is ex- 
tremely difficult, especially with regard to 
the value of the figures of the quotient, we 
shall here give a general rule for ascertain- 
ing their values, viz. 
Rule, place the first multiple of the divi- 
sor under the dividend, as in operations of 
common division ; then will the unit’s place 
of this multiple stand under such a place of 
the dividend, as the first significant figure 
of the quotient is to be ; that is, the first 
significant figure of the quotient will be of 
the same name or value with the figure of 
the dividend which stands above the unit’s 
place of the multiple. 
This rule will hold in all cases. 1. When 
the number of decimals are equal in the di- 
visor and dividend, the quotient will be 
integers, or whole numbers ; for placing 
the first multiple of the divisor under the 
dividend, according to the rule. Ex. 1. 
8.45)295.75(35 
25.35 
4225 
4225 
The unit’s place 5, is found to stand under 
9, the place of tens in the dividend; so 
that 3, the first figure of the quotient, must 
be tens also, and 5, the next figure, units. 
2. When the number of decimals in the di- 
vidend, exceed those in the divisor, as. 
Ex. 2. ■ * 
34.3)780.516(32.12 
72.9 
Where 2, the unit’s place of the multiply 
of the divisor, stands under 8, the place of 
tens of the dividend ; whence 3, the first 
figure of the quotient, must be tens also ; 
and 2, the next figure, units ; so that the re- 
maining figures, 12, must be decimals. This 
is done, more shortly, by making as many 
figures of the quotient decimals, as there 
are more decimal places m the dividend 
than in the divisor. 3. When there are not 
so many decimal places in the dividend, as 
there are in the divisor, cyphers must be 
added to the right hand of the dividend, to 
make them equal : thus, to divide 192.1 by 
7.684, as m E». 3. 7 
7.684)192.100(25 
15.368 
38420 
38420 
Add two cyphers to make the decimals 
equal ; and, by the above rule, the quotient 
25 will be found to be integers, as 5, the 
place of units, stands under 9, the place of 
