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TABLE.

OC, Thousands

X Thousands
* Thousands
c, Hundreds
o Tenth Parts
cHundreth Parts
* Thousand Parts
i X. Thou. Parts

C. Thou. Parts
- Units
a Tens

Q. May not Cyphers sometimes be annexed to Decimals?

A. They may, but they alter not their value: Thus, .44 and 4100 are the same.

Q. May not Cyphers sometimes be prefixed to Decimal Parts?

A. Yes; and then they decrease their Value by removing them farther from the point: thus .0041 is less than .41.

OF ADDITION AND SUBTRACTION OF DECIMALS.

2.How are Decimals added or subtracted?

A Place the numbers according to their value, and work as in addition or Subtraction of whole numbers.

Q. How are the operations proved ?
A. As in whole numbers.

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Shillings. 14.471 1.191 1.8126 3.6126 7,1281 18.8 126

Yds.
47.4

Gallons.
7004.16
712.712
19.0174

L. 71.001 120.07 31.1291

19.71 461.721 400.004

7.1004
707

7.3126
70.1851
3.108

13.4101 76.04 7.3

Miles. 41.8101 140.037 18.10

7.8141 16.4612 7.81

16. .16.18104

3.14 1.181 7.7121 8.19817 13.071

Acres.
.61271
.8712
2012
.87
.04
.4.

Ounces. 48.9108 1.8191 3.1080

.7012 ..0012 *0018

EXAMPLES IN SUBTRACTION.
Years.
Duys.

Weeks.
From 1081.761 712.10009

127.19 Take 10.00012 7.121

121.

Hours. 12.

.12

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Q. How are Decimals multiplied ?

A. As whole numbers are.

Note 1. Wien numbers are Multiplied, make as many decimal parts in the product as there are in two Factors taken together.

2. If Decinal places are wanted in the product, supply them with cyphers to the decimal point. 3. Observe the saine Nole here, which is given in Multiplication of Vulgar Fractions.

Q. How are the following examples proved ?
A. By inverting the Factors.

EXAMPLES.

1 Multiply .612 by 4. 12
2 Multiply 48. by :48
3 Multiply 37.9 by 46.5
4. Multiply .121 by 17.2
5 Multiply 1.81 by 71
6 Multiply 4.1 by 1.42
7. Multiply.00071 by .21

8 Multiply .00041 by .0007 9 Multiply .0027 by 4.1. 10 Multiply 410. by .0012 11 Multiply .07

by .07 12 Multiply 1.007 by .04! 13 Multiply 4.001 ly .004 14 Multiply 004 by .204

OF DIVISION OF DECIMALS. Q. How are Decimals divided ? .1. As whole Numbers are.

Note 1. The Decimal places of the Divisor and Quoriont must always be equal to those in the Dividend,

2. If there be more Decimals in the Diviser than in the Divadend, unner' (is rilany Cyphers as you please to the Dividend, sq $1.s to be equal ai least to the Divisur.

3 of Decimal Places are wonting in the Quotient, they must be supplied with Cyphers to the Decimal Point.

4. Observe the satile Note here, which is given in Division of Pidgar Fractions.

2. Ilow are the following examples to be proved? 1. By Multiplication.

EXAMPLES 1 Divide -19.4 by 37.5 7 Divide 9. hy .7121 2 Divide 47121.1 ly 47. 8 Divide 9. ů Divide 4.18 by .1812 9 Divide 14. by 47.31 4 Divisle .76121 by 41. 10 Divide 1. by 863. 5 Divide .612812 lay 7.21 1 Divide .01281 by .12 o Divide .121819 by .721 12 Divide.00012:12 by.018

by .9

OF REDUCTION OF DECIMALS.

GASE 1.

0. How do you reducs a Vulgar Fraction to a De. vinal?

14. Divide the upper Term by the lower.
Note i. Both Terms are to be esteemed whole Numbers.

2 By this Case, Tobles contuining the Decima! Parts of an Ilieger ure constructed.

EXAMPLES.

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to a decimal.

Facit 19230764 2 Reduce to a Decimal.

Facit ,1785714+Reduce 11 of 1: io a Decimal. Facit .6043956 to 4 Reduce 7s 6d to the Decimal of a pound. Facit 3751.

5 Reduce 10s 9d to the Decimal of a pound. Facit -5854167-1..

Neduce 24 Grains to the Decimal of a lb. Troy. Facit (0:1666-4.

7. Reduce 14 drams to the Decimal of a lb. Avoirdupois. Facit .0546875 lb.

8. Reduce 4 C. 2 qts. to the Decimal of a ton. Facit 225 T.

9. Reduce 14 C. to the Decimal of a ton. Facit .7 ton.

10. Reduce 174 drams to the decimal of an C. Facit .0060686+C.

11 Reduce 4 inches to the Decimal of a yard. Facit .1111111+yard.

12 Reduce 76 yards to the Decimal of a mile. Facit ,043181+ mile.

13. Reducé a mile to the Decimal of a league. Facit 33333333+ league.

14 Reduce 3 qrs. 2na. to the Decimal of a yard. Facit .875 yd.

15 Reduce 4 perches to the Decimal of an acre. Facit 025 acre.

16 Reduce pint to the Decimal of a gallon Facit .125 gal.

17 Reduce 1 gallon of wine to the Decimal of a hhd. Facit .015873+bhd.

18 Reduce 7 minutes to the Decimal of a day. Facit .0048611+day.

19 Reduce 2 days to the Decimal of a week. Facit .2857142+ week.

20 Reduce 72 days to the Decimal of a year. Facit .1972602 + year.

CASE 2.

Q. How do you find the proper quantity of a Decimal Fraction in the known parts of an Integer?

A. Multiply it by the common parts of the Integer.
Q. How do you prove Questions in this case ?
A. By Case 1.

EXAMPLES.

1. What is the proper quantity of .76 of a Pound ? Ans. 158 2d 1.6qr:

2. What is the proper quantity of 861 of a C. weight? Ans. 3 qrs. 121b. 6oz. 14.592dr.

3. What is the proper quantity of .461 of a shilling? Ans 5d. 2.128 qrs.

4. What is the proper quantity of .761. of a hhd. of wine ? Ans. 47 gals. 3 qts. 1.344 pt.

5 What is the proper quantity of .17 of a tun of wine ? Ans 62 gals. 3.36 qts.

6 What is the proper quantity of .761 of a day? Ans. 18 hrs. 15 min. 50.4 sec.

7. What is the proper quantity of .7 of a pound of silver? Ans. 8 oz. 8 dwts.

8. What is the proper quantity of .71 of 4 oz. of gold ? Ans. 2 oz. 16 dwts. 19.2 gr.

9 W bat is the proper quantity of .67 of a league ? Ans. 2 miles, c fur. 3 poles, 1 yd. o feet, 3 in. 1.8 b. c.

10. What is the proper quantity of .712 of a furlong? Ans. 28 poles, 2 yards, 1 foot, 11.04 in.

11 What is the proper quantity of .07 of a barrel of ale ? Ans. 2 gals. 1.92 pt.

12 What is the proper quantity of .4712 of an ell Eng. lish? Ans. 2 qrs. 1.424 na.

13 What is the proper quantity of .72 of a hhd. of Beer? Ans. 38 gals. 3.52 qts.

14 What is the proper quantity of .61 of a tun of wine ? Ans. 2 hhds. 27 gals. 2 qrts. 1.76 pt.

15 What is the proper quantity of .092 of 3 acres, 2 roods ? Ans. 1 rood, 11.52 poles.

16 What is the proper quantity of .461 of a chaldron of coals? Ans. 16 bush. 2.384 pecks. i7 What is the proper quantity of .712 of 3 qrs.

of corn ? Ans. 17 bush. 2.816 qrs.

18 What is the proper quantity of .3 of a year? Ans. 109 days, 12 hrs.

19. What is the proper quantity of .5 of an hour ? Ans. 30 min.

20 A certain Tenant hired an House for 9 years, at 12.41. per annum; how much was due at the end of the term ? Ans. 1111 12s. Note 1, To this Case is referred Case 4'in Practice, p. 55.

EXAMPLES.

1286 at 4s. Ist 4 21. 2d 1286

Facit 2571 45 ;

257.2

20

4

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