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2. What is the value of •679 of a shilling? Ans. 8.148d. 3. What is the value of .9999£? Ang. 195. 1140.79 or £1. 4. What is the value of .617 of a Cwt. ?

Ans. 2qrs. 131b. 1oz. 10,4 dr. 5. What is the value of -8593 of a lb. Troy!

Ans. 10oz. 6pwt. 5gr. 6. What is the value of 397 of a yard ? Ans. Iqr. 2.3521. 7. What is the value of •8469 of a degree ?

Ans. 58m. 6fur. 35po. Oft. 1lio. 8. What is the value of •569 of a year?

Ans. 207da. 16ho. 26m. 24sec. 9. What is the value of •713 of a day? Ans. 176. 6m. 43sec.

CASE V.
To find the value of any decimal of a pound by inspection.

Rule. Double the first figure, or place of tenths, for shillings, and it the second figure be 5, or more than 5, reckon another sbilling ; then, after the 5 is deducted, call the figures in the second and third places so many farthings, abating 1 when they are above 12, and 2 when above 36, and the result will be the answer.

Note. When the Decimal has but 2 figures, if any thing remain after the shillings are taken out, a cypher must be addexed to the right hand, or supposed to be so.

EXAMPLES. 1. Find the value of .876£ by inspection. 16s.

double of 8. Is.

for the 5 in the second place, which is to be taken And 6 d.=26 farthings remain to be added. (out of 7 Deduct d. for the excess of 12.

175. 6 d. tbe Ans. 2. Find, by inspection, the value of 49 £.

= double of 4.

for the 5 in the place of hundredths.

10d. = 40 farthings, a 0 being annexed to the remaining 4. Ded. d. for the excess of 36.

89. 1s.

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9s. 9 d. the Answer. 3. Find the value of .097£ by Inspection. Ans. 11. 11 d.

4. Value the following decimals by lospection, and find their sum, viz. 785£ + •537£ + .916.£ + .74£ t •5£ t .25£ + 09£ t .008£.

Ans. £3 16s. 6d.

As this rule is the reverse of the rule, Case III. che reason is apparc'ar from the demonstration of that rule.

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DECIMAL TABLES OF COIN, WEIGHT, AND MEASURE.

TABLE III, Pounds. Decimals. Ounces. Decimals.
TABLE I,

TROY WEIGHT. 27 241071 12 75
Coin.
Ilb. the Integer. 26

232143 11 £ 1 the lateger. Ounces the same as

25 "223214 IO

.625 Shil. dec.Shil dec. TABLE II.

"214286 9

5625 19! 95 9:45| Pats. Decimals. 23 *205357

8 5 18 9 IO *041666

196428 7 4375 17 85 71 35 9 '0375 21 '1875

6

*375 161 8

3

8

*033333 20 •178971 5 3125 19751 5.25

·029166 19

•109643

4 25 14) 7

*025
18 • •160714 3

•1875 13) 65 31 '15

5
'020833 17 '151786

*125 121 6 21 '1

016666 16 •142857 1 •o625 'SS 1 '05 3 0125

13 *133928 Drams. Decimals. IO 2 '008333 14 '125

15 *038593 Pence. Decimals, *004166 13 • '110671

'054687 11 *045833 Grains. Decimale.

12
*107143

13 'ogo781 IO •C41666

II
I 2 *001083

*098214

12 046875 9 *0375

10 089286 11 *00191

II

·042968 8

*001736
9 •080357

IO ·039062
·029166
'*001562

*071428

9 *035156 '025 8 •001389

7

*0625 7

8.

03125
*020833
s

6
001215
053571

*027343
*016666
6

Z
5
'O01042
*044643 6

023437
3
0125

·000868
4 *035714

S *019531 '008333

•ooo694
3 *036786

4 .015625 *004166

2 3 *000521

'0r7857

'011718 Farth's./Decimals.

*000347
'008928

'007812 3 *003125

*000173 Ounces. Decimals. '003906 2 •00208331 i Oz. the Integer.

IS '008370 TABLE VI. 1 *0010416 Peonyweights the

14 *007812 CLOTHMEASUURE. fame as Shillings in

13 •007254 1 Yard the Integer. TABLE II. Ithe first Table.

12 *006696

Qrs. Decimals. Grains. Decimalo.

•oo6138

3 Coin & Long Meas.

75
10 00558
I 2 *025

2

'S i Shil and 1 Foot

022916

9 II

003012

*25

8 the lateger.

·020833

*004464 10

Nails. Decimals. 9

*003906 Pence & 01875

3 Decimals. 8

•1875 6 '003348

016666 Inches.

125

s *00279

1 *0625
It
6 0125

4 *002232
10 833333
S 010416

3

TABLE VII.

'001674 9 75

2 4

.com/16 LONG MEASURE.

·008333 8 .666666

1 3 *00625

*000558 1 Mile the Integer. 7 •583333

Yards. Dccimals. *004166 gr.ofozs. Decimals. 6 '5 I *002083

'568182

3 '4166661.

*000418

900 *511364

2 *000279 4 *333333 TABLE IV.

800 *000139

454545 3 23

700 397727 2 266666 AVOIR DUPOIS Wt. TABLE V.

600

31 •0833331121b. the Integer. ib. the Integer.

AVOIRDU POIS Wt.

500

•284091 Farth's. Decimals.

400 *227 272 Ounces. Decimals. Qrs. (Decimals. 3 '0625

300 170454 3 *75

IS ·041666

9375

200 •513635 14 5

875 ·010383

100 096913 *25

Carried over.

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Yards. Decimals. TABLE VIII.

Days.) Decimals. 051136

30 LIQUID MEASURE.

•082192

Hours, Decimals. •045454

20 054794

11 478333 70 .0.39773 i Gal. the Integer.

10
·027397

10 416666 60 034091

9 Quarts the same as

·024657

375 50 023409

8 021918 40 022727

qrs. in TABLE VI.
i Pint.

7

7
125
019178

*291666 30 017045

6 Gills.) 09375

016438

6 25 20 011364

.0625
2
5 013698

• 208333 10 ·005682

010359

4 •166666 03125 9 .005114

3 -008219

3

•125 .0045 15

2 TABLE IX.

2 ·005479

•083333 .003977

1 5002739 1 041666 003109

Time. .002841

1 Year the Integer. 1 Day the Integer.minutes. Decimals. .002273

Months the same as 3 .001704 Pence in Table II.

Hours.) Decimals. 30 020333 2 .001136

23 •958333 20 013388 1 .000568 Days. Decimals.

22 .916666 10 .006941 365 1000000 Feet . Decimals.

21
•875

00625 300 .821928 20 .833333

8 ·005555 -0003737 200 -547945 19 791666

.004861 *0001892 100 •273973 18 .75

6 .004166 Inches. Decimals. 90 .246575 17 708333 5 003472 6 0000947 80 •219178

16 -666666

.002777 5 000079 70 •191781

15 •625

3 ·002083 .0000632 1 60 .164383 14 -583333

2 .001333 -0000474 50 •136936

13 541666

.000694 2 -0000316 40 109589 12 -5 1 -0000158

- నిలు 4 60 12.30

GENERAL RULE.

To find the value of goods in Federal Money.--Multiply the price and quantity together; point off in the product, for denominations lower than dollars, as many places as there are in the give en price; or, if there be decimal places in the quantity also, according to the rule for multiptlication of decimals. This is really roultiplication of decimals, the dollar being considered the unit:

EXAMPLES.

1. Find the cost of 823 yards, at $1.29c. a yard.

823X$1.29c. =$1061.67c, Ans. 2. Find the value of 56yds. 2qrs. at $3.11c. per yard.

56yds. Oqrs.=56:5; and 56:5X3:11=$175.710, 5m. Ans. 3. What'must I pay for 6 yds. at $5.50c. per yard'

Ans. $33.68c. 7m. •5. 4. Bought 7!yds. at 34 cents per yard: what did I pay for the hole ?

Ans. $2.62;;c.

COMPOUND MULTIPLICATION*

And as

IS extremely useful in finding the value of Goods, &c. in Compound Addition, we carry from the lowest denomination to the next higher, so we begin and carry in Compound Multiplication : One general rule being to multiply the price by the quantity. The reason of the following rules is obvious.

CASE I. When the quantity does not exceed 12 yards, pounds, &c: Set down the price of 1, and place the quantity underneath the least denomination, for the multiplier, and, in multiplying by it, observe the same rules for carrying from one denomination to another as in Compound Addition.

INTRODUCTORY EXAMPLES.
1.

2.
3.

4.
£ d. £

d. D. d.

£

d. Multiply 15 17 1 25 12 8 3 51 7 67

13 6 by 2 3 4

5

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In the last example, I say, 9 times 1 is 9 farthings=d. I set down and carry 2, saying, 9 times 8 is 72, and 2 I carry makes 74 pence,=6s. 2d.

| set down 2 in the pence and carry 6; then, 9 times 7 (the unit figure in the shillings) is 63, and 6 I carry is 69,

* The product of a number, consisting of several parts or denominations, hy auy simple number whatever, will be expressed by taking the product of that fimple number, and each part by itself, as so many diftinct questions : Thus £33 158. d. multiplied by :), will be 165 7 is. 4.id.=(by taking the shillings from the pence, and the pounds from the Thillings, and placing them in the Shillings and pounds respectively,) £108 14 s. 9d. and this will be true when the multiplicand is any compound number whatever.

I set down 9 under the unit figure of the shillings, and carry 6, saying, 9 times 1 is 9, and 6 I carry is 15, then I halve 15, which is 7 and 1 over, which I set in the ten's place in the shillings, and that, with the 9, makes 19 shillings; then I carry the 7 as pounds : Lastly, 9 times 4 is 36, and 7 I carry, are 43 pounds : I set down 3 and carry 4, saying, 9 times 1 is 9, and 4 I carry makes 13, which I set down, and the product is £133 198. 27d.

PRACTICAL QUESTIONS. Note. The facility of reckoning in the Federal Money compared with pounds, shillings, &c. may be seen from the examples in this aud The following cases ; where the same questions are given in both the currencies, as near as can be, avoiding small fractions.

In the following examples in this and ibe succeeding cases, the price in pounds, or shillings, &c. is in the currency of New Jersey, Pennsylvania, Delaware, and Maryland, where the dollar is 7s.6d. in the last example in each case ; in the last example but one, the price is in the currency of New York and North Carolina, where ihe dollar is 8s. ; and in the other examples, in the currency of New England, where the dollar is 6s. Thus in the 3d example, the price, 9s. 10d. in the currency of New York, &c. is equal to 122c. 9m. ; and in example 1th, the price 135.7}d.=181c. 7m.

53. 4d. 1. What will 9 yards of cloth at

83c. 9m. per yard, come to ? £0 53. 4d. price of one yard, •880. Im. Multiplied by 9 yards.

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$2 55c. 6m. per yard

Ans. £2 8 0 price of 9 yds.

$8.00

1 15s. 4d. 2. 3 yards at

S £265.

$7 66c. 8m. 95. 10d.

£2 199. 3. 6 $1 22c. 9m.

$7 37c. 4m.
13g. 70.

£6 2s. 7 d.
9
$1 81c. 7m.

$16 35c. 3m.

CASE II. When the multiplier, that is, the quantity, is above 12: You must multiply by two such numbers, as, when multiplied together, will produce the given quantity.

EXAMPLES.

3s. 511. 1. What will 144 yards of cloth cost at

£ 8. d.

0 3 57 price of 1 yard. •5764 Or, •5764 Multiply by 12

144

12

{

sic.6 cm. Sper yard?

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69168

12

Produces

2 1 6 price of 12 yards. 23056 Multiplied by 12

23056

5764 Answer £24 18 O price of 144 yards.

Ans. 983-0016

83.0016

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