CONTRACTED DIVISION OF DECIMALS:

RULE.

When you perform the operation to find the first figure of the quotient, let the remainder stand for a new dividend, without increasing it by bringing a figure or figures from the given dividend; do so in each case, pointing off one figure from the right of the divisor for each new dividend, observing at each operation, to carry the increase of the figures cut off, in multiplication, and the quotient will be had nearly

true.

EXAMPLE,

Divide 14169.206623851 by 384.672158 384.672158)14169.206623851 (36.8345+ Ans, 11540 16474

262904188

230803294

32100894

30773772

1327122

1154016

173106

153868

19238

19233

5.

EXAMPLES,

SHEWING COMMON PRACTICAL USES OF DECIMALS.

Ans. $187.50.

1. What will a piece of cloth, containing 50 yards, come to at $3.75 per yard? 2. What will 750 shingles thousand?

₹

come to at $12. per Ans. Ans. $9.

3. What will 15.450 feet of boards come to at

$15.50 per thousand?

Ans. $239.471

4. What will 350 gallons of whiskey come to at 8.75 per gallon? Ans. $262,50

5. What will 200 bushels of wheat come to at $1.60 per bushel?

Ans. $320. 6. What does the interest of $1575 come to in one year, at 5, 5, and 6 per cent? Ans. $259.87 Operation, 1575 X.05 =78.75

1575 X.055-86.62.5 Ans.

1575 X.06 94.50

NOTE. Decimal Arithmetic should be carefully studied by every student that would be a man of business. It is applicable to almost all kinds of computations. Our money unit being in a decuple, or tenfold ratio, makes it indispensably necessary to be. acquainted with decimals. A thorough knowledge of vulgar fractions should be previously studied, being the radix from whence decimals flow.

RULE OF THREE IN DECIMALS.

The Rule of Three in decimals is subject to the same rules as that of whole numbers..

EXAMPLES.

1. If 3.25lb. of flour cost 9.5cts, what would a barrel of flour come to, the weight being 196.b.

2. If .75 of a ton of iron cost $80.50, what is the price of 9.5 tons?

D..

D.

3. If .875 of a pipe of wine cost $104.25, what would a ton come to?

Pi. T. D.

.875

D.

1: 104.25: 238.284 Ans.

4. .375 of a farm contained exactly 100 acres, how many acres would 4.75 such tracts contain? Ans. 1266 acres. 5. .0625 of a cargo of tea came to $100; required, the amount of the whole. Ans. $1600.If a man spend .125 of his estate in 2.5 years, how long will the whole last him?. Ans. 20 years

6:

CIRCULATING DECIMALS:

A circulating decimal is, in other words, an indeterminate or unlimited decimal, representing only an approximate value for the vulgar fraction from which it arises; and is of such a nature, that it will sometimes repeat the same figure continually, or repeat every second, third, &c. in the same manner; from which arises the doctrine of simple, compound, and mixed repetends; similar, dissimilar, and conterminous. But as these quaint distinctions serve more for curiosity than real use, I shall content myself with barely giving some of the most prominent definitions.

The following fraction represents

A single repetend,

A compound repetend,

A mixed single repetend,

333333, &c.*

123123, &c..

.083333, &c.

A mixed compound repetend, .735145145, &c.

Similar repetends which begin at the same place,

are said to be conterminous.

.333 &c. and .111 &c. are similar repetends.. .333 &c. and .083 &c. are dissimilar.

NOTE. It is generally time to stop, when any decimal whatever, of any shape, runs to six places; being sufficiently accurate for all practical purposes.

NOTE 2. In calculations, where circulates are concerned, the first repeating figure is frequently marked with a dash drawn across it.

It may appear strange to a student, to hear it roundly maintained, that it is possible to shew the precise sum of a progression which consists of an infinite number of terms, when no one in existence can have a distinct idea of the magnitude of such a number. ; reduced to a decimal, will run on for ever, .333, &c. constantly approaching its ultimate, without being able to come up.. Hence a faint notion of infinity.

DOUBLE RULE OF THREE.

EXAMPLES.

1. If $100, in .75 year, gain $4.5 interest, what principal will give 89. in .25 year? Ans. $600. 2. If 40 men, in 19.5 days, earn $60.5; how many men, in 20 days, will earn $155? Ans. 100 men. 3. If 12 men mowed 15.5 acres of grass, in 15.5 hours, how many acres may be mowed by 100 men, in 2.25 hours? Ans. 18.75 acres.

EXTENSIVE ADDITIONS.

Such as frequently occur in bank, and other large monied establishments.

RULE.

Add each column by itself, and place the respective aggregates in such order, that units, tens, hundreds, &c. may stand in their proper places; lastly, add those aggregates together, and you have the whole sum.