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Example 1, What is the value of .564 of a pound sterling?
20 shillings in a pound Here I multiply the given 17,280 decimal by 20, the number of 12 pence in a fhilling parts of the next less denoni. 3,360
4 farthings in a penny nation, viz. shillings, and from
1,440 the product I separate the three figures on the right hand, 280, Answer 11s. 31d. 440 of a as there are Noree places of farthing decimals in the given nuinber.
I then multiply these separated figures 280 by 12, and from the product 3360 I separate the three first figures 360, as before, to be multiplied by the parts of the next denomination, viz. 4; then the figures standing on the left hand of these separated figures will be the answer.—115. 31d.
The same rule serves lo discover the value of any other integers, having regard to the number of parts.contained in ach inferior denomination.
Thus to find the value of a decimal fraction of a pound troy, I first multiply the fraction by 12 to find the ounces, then the separated figures by 20 to find the peanyweights, and lastly by 24 to discover the grains.
Q4.2. What is the value of .6725 of a cwt. ? - Answer 29rs. 19.b. 5oz.
Qu. 3. What is the value of .61 of a ton of wine :Anf. 2hhds. 2 7galls. 2qts. ipt.
Cafe 3. To find the value of a decimal of a pound sterling, by inspection.
Rule. Double the first figure of the decimal on the left hand for shillings; and if the next figure be 5, or above 5, add 1 shilling more to it: then call the figures in the second and third places farthings (after deducting 5 from the second figure if necessary), and if the number of farthings be above 12 abate one, and if above 37 abate 2. The other figures in the fraction, if more, are negleted.
Example 1. Find the value of .564 of a pound by inspection.
Here I take the double of For the 5 take 5, the first figure, for Chillings, For the Š in the 6 take i which is so, also i shilling
For the 14 remaining o 31
34 inore for the 5 contained in the 6, and the remaining 14 (viz. 1 in the 6, and 4) I consider as farthings, abating 1 because they are above 12, which make 31d. : thus the decimal .564 of a pound is 11s. 31d. as may be seen in Cafe 4.
Qu. 2. Find the value of .7880 of a pound by inspection, -Aufwer 155.gd. Qu. 3. Find the value of .14729 of a pound by inspection, Anf. 25. 114d.
Cafe 4. To find the decimal fraction of a pound equal to any given number of shillings and pence.
Rule. Write half the greatest even number of shillings for the first figure in the decimal, and the number of farthings in the pence and farthings for the second and third figures, observing to add 5 more to the second figure, if the number of shillings be odd; also add one more to the third figure, if the farthings exceed 12, and add z if they
Example 1. Find the decimal fraction of a pound equal to 115, 31d. Here for the 11s. I take of For half 1o take
.5 the next greatest even number,
For the odd shilling .05
.014 which is 5, for the first figure
•564 of the decimal, and for the odd fhilling, place 5 to be added to the second figure; then for the 31d. I take 14 to be added to the second and third numbers, as there are 13 farthings in 31d. and 1 is added, as the farthings are above 12 ; thus, the deciinal is .564 of a pound.
Qu. 2. Find the decimal equal to 185. 4£d. -- Ans. .919.
Qu. 3. Find the decimal equal to 175. 614.-Anf. .878. VOL. I.
OF ADDITION OF DECIMALS.
ADDITION of decimal fra&tions is performed in the fame manner as addition of whole numbers, except in the diípofition of the figures.
Rule. Place the figures exactly under each other, according to the value of their places, that is, the whole numbers (if any) under each other, as in addition of whole numbers, and the fractions are alfo to be placed according to their values, viz. primes under primes, feconds under seconds, &c.
Then find their fum as in whole numbers, and point off as many places for decimals as are equal to the greatest number of decimal places in any of the given numbers.
Example 1. What is the sum of 22.5709, 1.03, 1492.00, 2.971, .00726?
22.5709 Here the numbers are added together like 1.03 whole numbers, and the number of places 1492.001 pointed off for decimals are 5, equal to the
.00726 greatest number of decimal places in any of
1518.58016 the given numbers. The figures on the left hand of the decimal point are whole numbers or integers.
OF SUBTRACTION OF DECIMALS.
Decimal fractions are subtracted in the same manner as whole numbers, but the numbers are placed and the decimals pointed off according to the rule given in the foregoing fection.
Example 1. What is the difference of 247.0729 and 3746.805732?
Here the uppermost number consists of 6 3746.805732 places of decimals, wherefore the remainder 247.0729 sought must have as many deeinial places; in 3499.732832 every other respect it is wrought like fubtraction of whole numbers.
OF MULTIPLICATION OF DECIMALS.
RULE. Multiply the given numbers one by the other, as in whole numbers.
Then point off as many figures for decimals as there are decimal places in both the numbers ; but if there be not so many places in the product, as many cyphers must be prefixed on the left hand thereof as will make up the number of decimal places required. Example 1. Multiply 2 03271 by .0056.
In this example the number of decimal
2.03271 places in both the multiplier and multiplicand
.0056 is 9; but the product consists of only 8
1016355 figures, therefore I must prefix one cypher
.011383176 on the left hand thereof, which makes the true product.
.43970 540 58860
154 30380 S10882 900
1983 906 10811772
6613 02 116.23195 48860
88173 6 .96924 82980
Thus it appears that in multiplication of decimal fractions there is no necessity for placing those figures of the same value under each other, as in the two foregoing rules *.
OF DIVISION OF DECIMALS.
This rule is also performed as division of whole numbers, but from the quotient point off as many figures for decimals as the decimal places in the dividend exceed those in the divisor, But if the places in the quotient be not so many as should be pointed off for decimals, as many cyphers must be placed on the left hand as necessary.
* There is a contracted method of working both this and the following rule given by many writers on arithmetic. They are, however, not very simple, and may very well be superseded, by omitting some of the decimals in both numbers, and working according to the general rule.