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Case 3d. To reduce numbers of different names to their equivalent decimal values.

RULE.

Place down the lowest name mentioned. Divide this by as many as make one of the next higher denomination, annexing ciphers to the dividend as you require.

Before this quotient place the next higher name, and divide by as many as make one of the next higher denomination. And so on throughout, and the last quotient is the decimal required.

Here, the lowest name is 3 fgs. Example.

divided by 4, because 4 fgs.=1d., Reduce 9s. 2 d. to the decimal with two ciphers annexed to the of a pound.

dividend. 4) 3.00

The next higher name is 2d., 12) 2.75

which is placed before . 75. 2.75

is divided by 12, (12d.=1 sg.) 20) 9.22916, &c.

To this quotient 9 is placed, . 461458, &c.

and 9.22916 is lastly divided by

20, (20 sgs. = 1 £). So that Answer, . 461458 of a £.

9s. 2 d. =461458 millionths of a

pound. Another Example. Reduce 2 qrs. 7 lb. 8 oz. to the

The lowest name is 8 oz. didecimal of a Cwt.

vided by 16, (16 oz. = 1 lb.) 8.

The next higher name is 7 lb., 4)

which is placed before .5. 7.5 is 16 2.

divided by 28, (28 lb. =1 qr.), and 7.5

to this quotient the 2 qrs. are 4)

placed. Lastly, 2.267857 is di28 1.875

vided by 4, (4 qrs.=1 Cwt.) So 2.267857

that 2 qrs. 7 lbs. 8 oz.=566964

millionths of a Cwt. .566964, &c.

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4)

Answer, .566964, &c. of a Cwt.
This and the last Case prove each other.

Proof of the preceding Example by the last Case.
What is the equivalent of .566964, &c. of a Cwt.

.566964, &c.

2.267857 (with Remainder.)

28

2142860 (with Remainder.)
535714

7.500000

16

8.0

Answer, 2 qrs. 7 lb. 8 oz.

CISES. 59. Reduce 94d. to the decimal of a shilling.

Answer, .791666, &c. 60. Reduce 14s. 6d. to the decimal of a £.

Answer, .725 61. Reduce 17s. 54d. to the decimal of a £. Answer, .871875 62. Reduce 5 oz. 12 dwts. 7 grs. to the decimal of a pound troy.

Answer, .4678819, &c. 63. Reduce 1 rood, 30 poles, to the decimal of an acre.

Answer, .4375 64. Reduce 3 qrs. 18 lb. to the decimal of a Cwt.

Answer, .910714 65. Reduce 3 bush. 1 pk. to the decimal of a quarter.

Answer. .40625 66. Reduce 1 qr. 1 nl. to the decimal of a yard. Answer, .3125 67. Reduce 3 weeks, 6 days to the decimal of a month.

Answer, .964285, &c. 68. Reduce 7s. 101d. to the decimal of a guinea. Answer, .375 69. Reduce 18s. 11 d. to the decimal of a pound.

Answer, . 948958, &c. 70. Reduce 3 qrs. 17 lbs. 9 oz. 15 dr. to the decimal of a Cwt.

Answer, .907331, &c.

RULE OF THREE IN DECIMALS.

Rule. If the given numbers require it, reduce them to decimals by the last Case.

State the question, as in the common Rule of Three :multiply the second and third terms together, and divide by the first :-the quotient is the answer, in the same name as that to which the last term was reduced.

Example.
If 5 Cwt. 2 qrs. 16 lb. of Sugar cost £25. 18s. 9fd., what cost 43 lb. ?
Ib.

lb.
fgs.

The three 16

4.5

2.

terms are first

4 28 4. 28 1.125

9.5

reduced to 7

7
12-

Decimals 2.571428

.160714 18.79166 4

20

by the last Cwt. 5. 64285 Cwt. .040178 £25.93958 Case.

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71. How much Pepper, at 1s. 4}d. per lb., can I buy for £12. 15s. 9d.?

Answer, 1 Cwt. 2 qrs. 18 lb. 72. If £250. 10s. gain £12. 10s. 6d. in 12 months, what principal will gain the same in 71 months ?

Answer, £400. 16s. 73. How much Stuff, f of a yard broad, will line 74 yards of Cloth, s of a yard broad?

Answer, 9 yards +.0416. 74. At £2. 19s. per ounce, what is the value of 19 oz. 3 dwts. 5 grs. ?

Answer, £56. 10s. 5 d. +.2981. 75. At 12s. 4d. per ell English, required the value of 49} yards.

Answer, £24. 5s. 11d.7.1984. 76. If silver be worth 4s. 7d. per ounce, what is the value of 2 lb. 5 oz. 17 dwts. 5 grs. ?

Answer, £6. 16s. 104d.+.2867. 77. If 4 yds. 3 qrs. of Cloth cost £1. 5s. 73d., how many yards can be purchased for £20. 13s. 9d. ?

Answer, 76 yds. 2 qrs. 3 nls. +.1216. 78. How many Cwt. of Sugar can be purchased for £36.75, at 9 d. per lb. ?

79. If 3} yards of Cloth were sold for 12s. 13d., what would be the cost of 7 pieces, each 25% yards ?

INVOLUTION.

Involution, or the raising of powers, is the method of finding the Square, Cube, &c. of any given number, and is performed by repeated multiplication.

Any number multiplied into itself produces the square, or second power; and that product, multiplied by the given number, produces the cube, or third power; and so on to any power

whatever. The number given to be involved, is called the Root, or

first power.

: the

The index, or exponent of a power, is the number which denotes the

power: square of 9 is often expressed 92 ; the cube of 8 as 83 ; the 4th power, or biquadrate of 23 as 234, &c.

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