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EXAMPLES.

i Reduce 155 8d. { to the decimal of a pound ; also, 3975, 12lb. 6oz. 14,592dr. to that of an C.wt.

grs. 15 81=7541 960)754;00(07854166%. +facit.' 20 0 =9603 6720

si di

2. gr.

1634

8200, &c. Ori

16 54 | 14,592 dr. 4

4 (3,648 12 8. 5d.

6,912 oz. 2,0 | 15. 7083335.

14 (1,728

28 4 1 12,432 16.
27854166+

27 (3,108
4 1 3,444 gr.
facit ,861 Ciwt.

2 Reduce 75 6d. to the decimal of a pound. facit ,375 3. Reduce gde to the decimal of a pound.

1.375 4 Reduce 10s 9d to the decimal of a pound.

15385416+ 5 Reduce 24 grains to the decimal of a .

,0041666+ 6 Reduce 14. drams to the decimal of a lb. avoirdupois

.

facit :0546875 7 Reduce 4C 2qr. to the decimal of a ton. facit 9225 8 Reduce 76 yards to the decimal of a mile.

,04318+ 9 Reduce 3qr. zna to the decimal of a yard. facit ,875 10 Reduce 4 perches to the decimal of an acre. facit ,025 Reduce pint to the decimal of a gallon.

,125 12 Reduce 7 minutes to the decimal of a day. ,00480+ 13 Reduce 36.wt. 2gr. 141b. to C.wt. 3,625C.wt. 14 Reduce 7yds. 2gr. zna, to yards.

7,6875yds. 15 Reduce 13A 1R 14P. to acres.

13,3375 A. 16 Reduce zino. 1w. 5da. to months. 3,42857+ moi

CASE

2 Who

CASE 3,
To reduce a decimal fraction to its value ;

RULE.
Multiply it by the known parts of the integer.
Note. To find the value of any decimal of a £. by inspection ; dou-

ble the first figure after the point for shillings, adding one, if the
fecond be 5 or upwards; the second, if less than 5, or its excess
above si call tens, and the third units of farthings, abating one
when above 12, and two if above 36.

EXAMPLE S.
I What is the value of ,7854166 of a pound?
97854166 By inspection.

20 ,7854166 .. 15,7083320

&. 15 8 2 12

That is 7+7+1=155. d. 8,499984 and 35-1 =3qrs.=8d.

=158 4 gr. 1,999936 answer 15 I 1,9999 is the value of ,76 of a pound?

answer 155 2d. 1,6qr. 3 What is the value of ,625 of a shilling? answer 7d. 4 What is the value of ,8322916 of a L.

answer 16s 7d. 5 What is the value of ,861 of an C.wt.?

answer 3qr. 121b. 6oz. 14,592dr. 6 What is the value of ,7 of a 16 troy? ans. 8oz. 8dwf. 7 What is the value of ,671 of a day?

answer 18hr. 15min. 50,4 sec. 8 What is the value of ,71 of 4 02. troy?

answer 20%. 16dwt. 19,2gr. 9 What is the value of ,76 of a league ?

answer 2M. 3pls lyd. 3in. 1,85.42 10 What is the value of ,4712 of an ell English?

answer 2qr. 1,424na.

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142 The Single Rule of Three in Decimals. 11 What is the value of ,092 of 3A. 2R ?

answer 1R. 11,52wer: 12 What is the value of ,3 of a year?

answer 109da. 13hr. 48min. 13 What is the value of ,6875 of a yard ?

answer 2qr. 3na. 14 What is the value of ,3375 of an acre ?

answer 1R.. 14per. 15 Find the value of ,785 of a 6. by inspection.

answer 15s 8d. 16 Find the value of ,875 of a £. by inspection.

answer 175 68. 17 What is the value of a tenement for nixe years, at 12,4l. per annum?

answer 1111 12s. 18 Sold 25 yards of superfine scarlet cloth, at 2,75l. per yard; what was its value?

answer 681 15s. 19 What is the sum of ,48 of a to, and ,16 of a shilling?

answer 9s 9,12d. 20 What is the sum of ,17 of a lb. troy, and ,84 of an oz,?

answer 20%. 17dwt. 14,4gr. 21 What is the surn of ,177. ,196.wt. ,17gr. ,716.

answer 3C.wt. 2qr. 15,541b. 22 What is the sum of 278 acres, and ,67 rood ?

answer. 3R. 31,6per. 23 What is the difference between ,171. and 78.?

answer 2s 8d. 1,6qr. 24 What is the difference between ,41 days, and ,16 of an hour?

answer Ohr. 40min. 48seci

THE SINGLE RULE OF THREE IN DECIMALS .

The operation both in direct and inverse proportions are agreeably to those rules in page 59, and 63, having regard to placing the points.

DIRECT PROPORTION.

EX A MPLES.
If 1,4lb. of mace cost 14,5s. what cost 75,3116?
Ib.

lb.
As 1,4 14,5 ; : 75,31.. 38 19 11 3,52 answer.

d. gr.

3 9,716.?

2 If 1,6C. of sugar sell for 31 12,76s. what is the proportional cost of 3hhds. each 11C. 39r. 10,12h.

answer 801 155 3d. 3,36qr. If 1,50z. of silver be worth 7,85. what is the value of

answer zol 5s 3d. 1,449r. 4 If 1947C. of sugar be worth 4,5l. what is that for 1,716?

answer 11,1d. 5 Sold 12,5hhds. of wine, at 1,25. per pint; query the amount?

ans wer 3781. 6 Bought 3 pieces of cloth, each 21,5 yards, at 12,35. per yard ; please to cast up the cost. facit 391 1354,2d.

7 If 8,416, of tobacco cost 16s 4,6d. what is the value of 3hhds. each 4C. 2qr. 7,416.

answer 1492 12s 3d. I 8 How many yards are in a piece of cloth which brings 6l 13,12s. at 45 2,6d. per yard? answer 31,569yds.

9 Bought 5,8 tons of oil for 60,41. whereof 50,9 gallons leaked out ; what must the rest be sold for per gallon, that the purchaser may be no loser ?

answer 10,27d. 10 A grocer bought 7,6C.wt of sugar, at 40,15. per C.wt. which he sold at 4,5d, per lb. whether did he gain or lose, and how much? answer gained 145 "5d. 1,129r.

11 Bought 36. 1,59r. of cloves, at 2,755. per Ib. which was sold for bol n is 6d. query the gain ? answer 81 12s.

12 When a merchant buys 436 yards of cloth at 8,55. per yard what will he gain by disposing of it at 10,755. per yard ?

answer 491.15. A owes B 296,851. but compounds for 7,55 in the £ what sum must B receive ? answer nill os 4d. 2qr.

14 How many English ells of linen may be bought for 257 18s id. at 7 d. per yard? answer 53E iqr.

15 If a yard of ribband sell for 4,5 cents, how many dollars will buy 345 yards ? ans. 15,525, i.e. 15 D. 5210.

Didi c. m 26 When 675 yards cost-12,8 2 5. how many yards may be had for 38 mills ?

answer 2 yards.

D. d. co 17. If 19 yards of calico bring 2597 5. what will 435,5 yards come to?

D. d. c.m. answer 590,2 1 777;

18. What

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144 The Single Rule of Three in Decimals.

18 What must be paid for 73 yds. of broad cloth, at si dollars per yard? answer 40,5625D. or 40D. 56cts.

19 How does broad cloth sell per yard, when 78 yards cost 40D. 564cents ?

answer 5,5D. 20 The French foot is just 1,068ft. English ; how tall then would a 6ft. Philadelphian be at Paris?

answer but 5,618j7.

INVERSE PROPORTION.

EX A M P L E S. How many men can do as much work in ,4 of a month, as 16 could in a month and a half?

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As 1,5 : 16:: 94: 60 answer. 2 If, when wheat flour is as high as 6l. per C.wt the half penny cake weighs 1,13330. what should be the weight of it, when flour is only 1,81251. per C.wt. ?

answer 3,7502.=30%, 12dr. 3 If a board be ,75 foot broad, what length will it require to measure 12 square feet ?

answer 13ft. 4 How much Persian ,75yd. wide, will line 25,5 yards of five quarter cloth?

answer 42,5 yds. 5 A han 40,7 yards of linen, for which В gave him 25,6 ells of Holland, valued at 4,55. per ell ; how was A's linen rated per yard?

answer 25 gd. 3,8gr. 6 How

many

dollars of 7,55. each, should be given in exchange for 100 French guineas, at 34,55 ? answer 460

7 What sum has A at interest, when it yields as much in 74 months, as B's 450l. do in 15? answer gool.

THE Double Role or THREE IN DECIMALS.

Questions in this rule are wrought as in whole nambers, placing the points agreeably to the preceding directions,

EXAMPLES. 1 If 3 men receive 8,91. for 19,5 days labour; how much must 20 meri have for 100,25 days ?

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