eS6 
arithmetic. 
whether it he coin, weight, meafure, or time, &c. as i 
pound, i (hilling', &c. is fuppofed to be divided into io 
equal parts, and each of thefe parts into 10 parts more, 
and To on by continual fubdivifion. 
A decimal fradtion is expreffed by prefixing a point near 
the top on the left of it. Thus -4 fignifies T 4 S , -04 fignifies 
5^0, ' 4-5 fignifies and -007 fignifies T ^. The follow¬ 
ing Table will farther illufirate the notation of decimals : 
Whole Numbers. 
( -^-> 
7 5 6 3 4 2i 
C o y; n 3 
Decimal Parts. 
- 
6 
784 
o 
D n> 
j/> p. 
O 
Q. 171 E Cl. ( 
-1 O 
‘ = Cu 
iJ Cl (/) 
R?o J 81 
•3 4 5 
’r! Ti *0 *rj *13 Tl T) 
5D p p y JU 61 W 
^ ^ ^ ^ 
t/j ^ to W t/) ^ 
c o o O o O O 
o 
H x, 
»■> 
0 3 
c fj- 
& 
3 
CL, 
° O 
o .0 
0 £ 
° 8 
r "937 
74-876 
•8472 
702-83 
0-4731 
46-761 
■706S7 
74-47 
0-7074 
447-476 
*67311 
8-76 
9-7476 
76-8073 
1-7 6 
13-698 
3-8073 
0-3767 
3-0873 
8 - 43 - 
1-0737 
67-462 
0-076 
370-077 
0-761 
18-9761 
7-0073 
0-464 
5/0407 
0-467 
0 * 74 I 09 
47-907 
.23-5478 
733-2021 
From .84 
Take -674 
Rem. -166 
In Subtraction, 
x -oooo 
o~ 3 8 49 
• 6151 
Proof -84 
•7 
•07777 
•62223 
•7 
•5 
•07575 
•42425 
•5 
What is the difference between 8-98 and '898 ? An- 
fwer, 8‘082. 
What number added to 10-037 will make it juft 100-37 ? 
Anfwer, 90-333. 
What is the difference between 74-8974 and 0-748974? 
Anfwer, 74-148426. 
What number added to 0-3748 will make it juft 98-1 ? 
Anfwer, 97-7252. 
MULTIPLICATION of DECIMALS. 
Ru le. Place the fadtors and multiply them as in whole 
numbers, and from the right hand of the produdt cut off* 
as many places for decimals as there are in both factors to¬ 
gether ; but, if there ftiould not be fo many places in the 
product, make up the number with cyphers to the left hand 
Ex. 
From this Table it appears, that as whole numbers in- 
ereafe in a tenfold proportion from the units place towards 
the left hand; fo do decimal parts decreafe in the fame 
proportion towards the right. And decimal parts are only 
Teparated and known from the whole numbers by a point, 
and take their name from their diftance below the units 
place tow-ards the right hand. 
{ 0-7 is 7 parts of ten 
°"75 is 75 parts of a hundred 
0-875 is 875 parts of a thoufand 
In any decimal fraction, the firft figure next the decimal 
point is greater in value than all the reft, as in the decimal 
•1999,99, the firft figure 1 is greater in value than -099999 ; 
and unity, or 1, is greater than -999999, &c. Cyphers to 
the right of a decimal neither increafe nor diminiih its va¬ 
lue, thus -4, -40, -400, See. are all equal, becaufe 
-2^^, &c. as is plain from vulgar fradtions ; and 
therefore decimals are foon reduced to a common denomi¬ 
nator by annexing cyphers. But cyphers prefixed to a de¬ 
cimal, diminifh its value by removing it farther from the 
decimal point, or units place. 
{ °"5 ’ s 5 pacts of ten 
0-05 is 5 parts of a hundred 
0.005 is 5 parts of a thoufand, &c. 
Confequently the true value of all decimal parts is ea- 
lily known by their diftance from the units place. 
ADDITION and SUBTRACTION of DECIMALS. 
Place all the decimal points diredtly under each other, 
and then add or fubtradt as in whole numbers ; and, laftly, 
put a point under the other points, which will mark off 
the number of decimal places, in the fum or difference. 
Examples in Addition. 
1. Multiply 
By 
382.46 
7 *423 
U 473 S 
76492 
152984 
267722 
Produdt 2839-00058 
Ex. 2. Mult. 0-03789 
By °*°3475 
18945 
26523 , 
J 5 l 56 
3 ° 3 t 2 
Produdt -0032111775 
To find the area of any redtangular figure, multiply the 
length into the breadth. Thus 53-09X53-09=2818-5481 
yards, the anfwer. 
Ex. What is the area of a redtangular field, whofe length 
is 8-95, and breadth 6-347, chains ? 
Thus, 8-95X6 - 347=56-8o565 fquare chains. 
When a decimal is to be multiplied into an unit with 
cyphers annexed, as 10, 100, 1000, &c. you are only to re¬ 
move the feparating point in the multiplicand fo many pla¬ 
ces towards the right hand as there are cyphers annexed 
to the unit, fubjoining cyphers if needful. 
The produdt of 5-738 by 10—57-38 
The produdt of 49-3 by 100=4930- 
The produdt of -0547 by 100000=5470- 
The produdt of -008359 by 1000=8-359 
In large decimals the work may be contradted by mul¬ 
tiplying by the figures of the multiplier in a contrary or¬ 
der; thus, multiply the whole multiplicand by the left- 
hand figure of the multiplier; then prick off the right- 
hand figure of the multiplicand, and multiply the reft by 
the next figure of the multiplier, fetting down the firft fi¬ 
gure of every produdt diredtly under each other. Then 
prick off the next right-hand figure of the multiplicand, 
and proceed as before ; and fo on to the end. At the be¬ 
ginning of each line obferve what is to be carried from the 
preceding figures fo pricked off, viz. x from 5 to 15, 2 from 
15 to 25, 3 from 25 to 35, and fo on. When you multiply 
by the units place, obferve what place of the multiplicand 
it begins with, and cut off fo many decimals in the pro- 
dudt. By this rule you may fet the units place fo as to 
have any required number of decimals in the produdt. Or 
obferve the places of any two decimals that begin the mul¬ 
tiplication, and the fum of them gives the number of de¬ 
cimals in the produdt. 
Ex. 
1. Multiply 
By 
What is the fum of 47-82, 8-692, 4times-8o7, 472-9, 
1-46, twice 9-07, and -0763? Anfwer, 552-3163. 
What is the fum of 7-69, 46-8607, -064, 5times4-S03, 
•3404, 4 times -0083, and twice -07603 ? Anfwer., 
79 * *5536 
83’57468 
6-41807 
50144808 
3342987 
83575 
66860 
585 
Ex. 2. Mult. 
By 
516-38815 
•8905738 
•0347596 
26717214 
3562295 
623402 
44529 
8010 
_ 534 
•030955984 
DIVISION 
