In counting decimals from left to right, they decrease in a tenfold proportion, with a view to give the decimal expression; but to enumerate them from right to left, they increase in a tenfold proportion, the same as whole numbers. Ciphers annexed to a decimal do not increase its value, as in whole numbers; their value is determined by their distance from the units' place, or decimal point; thus .1, or .10, are equal, being read one tenth and ten hundredths, which is the same; but when prefixed, that is, placed at the left of a figure, it decreases in a tenfold proportion, thus, .1 .01; in this position their value is different; figure 1 and 0 having changed places, it has decreased the value of 1 in a tenfold proportion, it being only one tenth part as much as figure .1; .5, .05, .005-10, 100, 1000, .75=2=70%, &c.

5

A mixed number is that which consists of a whole number and decimal, as 4.4, 21.42, 100.75, &c.

There are various kinds of decimals, such as circulating decimals; but the limits of this work will not permit a full investigation; neither does the occasion require it, suffice to say; in circulating decimals, if one figure only repeats, it is called a single repetend, as .1111, .6666, &c.

A compound repetend, thus: .0101, .379379, &c. There are a variety of examples under this head, but in most cases three or four places of decimals will be sufficient, unless great accuracy is required. We will now introduce decimals as applicable to the currency of this country, which in its nature and operations is purely decimal. The laws of our country require that all transactions in money, both as relates to government and individuals, shall be performed in dollars and cents, or, as it is termed, "federal currency." This currency increases and

decreases like decimals, in a tenfold proportion, thus :

- E. eagle.

It is customary with accountants to use only two of the above denominations, namely, Dollars and Cents, the cents being hundredths of a dollar; and the fractional part of a cent is expressed thus, one quarter;, one half; 2, three quarters of a cent; but it would be more correct to give the exact number of mills. There is but one difficulty in learning decimals-that is, where to place the decimal point or separatrix, which will depend entirely upon the nature of the question, for which there is a sufficient number of rules and examples; and in every other respect, their operation is the same as whole numbers.

AMERICAN COINS.

The Mill is not a coin, but the tenth part of a cent.

The Half-Cent is a copper coin, 200 being equal to one dollar.

The Cent is a copper coin, 100 being equal to one dollar. The Half-Dime is the smallest silver coin, being equal in value to 5 cents, or 20 to one dollar.

The Dime is a silver coin, being equal to 10 cents, or 10 to one dollar.

=

The Quarter-Dollar is a silver coin, 25 cents, or 4 to a dollar. The Half-Dollar is a silver coin, 50 cents, or 2 to a dollar. The Dollar is the largest silver coin, equal to 100 cents, of an Eagle.

The Quarter-Eagle is the smallest gold coin, =2D. 50cts. The Half-Eagle is a gold coin, =5D.

The Eagle is the largest gold coin. =10D.

The above coins, in their composition, are not of pure gold and silver, but composed in part of alloy, a table of which will be given in its proper place.

To write sums in dollars and cents, the dollars are placed at the left, and the cents at the right hand, separated by a period.

2 1 4 6.811

214681 .25

To reduce vents to dollars, divide by 100, or separate two

figures from the right, and those on the left will be dollars; to

Decimals.

change fourths of a cent to cents, divide by 4; to change halves of a cent to cents, divide by 2; to change thirds of a cent to cents, divide by 3; to change mills to dollars, divide by 1000, or separate three figures from the right of their number, thus: 1.000=1D.

5

25

Quest. When the following fractions occur, such as 1,120,

75

how is a unit supposed to be divided?

Ans. Into 10 equal

parts, called tenths; and each tenth into 10 other equal parts, called hundredths; and each hundredth into 10 more equal

parts, called thousandths, &c. Quest. How will you write them down so as to give the decimal expression? Ans. By taking away the denominator, and placing a period, or decimal point, before the numerator, thus: ·.5, .25, .75, .8, .2, &c. Quest. What is the use of a decimal point in fractions? Ans. It shows the place of the units, and separates the fraction from the figures at the left (if any) which are whole numbers, and may be called the separatrix. Quest. Write down (7 hundredths) decimally. Ans. .07, also Too,=.008 and 1000= =.004=eight thousandths and four thousandths. Quest. How do decimals decrease in value from left to right? Quest. How do you determine the value of a decimal? Ans. By its distance from the decimal point.

For a more full and perfect explanation of fractions, see Vulgar Fractions, which, if the teacher please, can follow decimals.

ADDITION OF DECIMALS.

RULE.

1. Write down the numbers under each other, observing to place tenths under tenths, hundredths under hundreths, &c Be particular that the decimal points stand directly under each other in a perpendicular line, both in the given number and in the sum. 2. Then perform the operation the same as in Simple Addition. Proof-as Simple Addition.

41 .653 46 .23456 12 .3456 48 .9108 21 .037 49 .607

36 05 24 .90400 7 .891 24 .009 17 .00411 2 .34

1..6

3 .01111

5.6

1 .8191 15 .122 50 .421 3.1030 12 .042 18 .1610 .7012 10 .120 71 .65843

103 .312 91 .15378 28 .1766 54 .5341 58 .321

7. Add 12.34565+7 .891+2 .34+14 .0011 together.

Ans. 36 57775.

8. Add .7509+ 0074+.69+.8408+.6109 together.

9. Add .7569+.25+.654+.199 together.

Ans. 2 .9000.
Ans. 1 .8599

10. Add 71 .467+27 .94+16 .084+98 .009+86 .5 together.

11. Add to 9 .999999 the millionth part of a unit.

Ans. 300 .000.

Ans. 10 .000000

15.

12.

D. c. m. D.

d. c. m. D. d. c. m. E. D. d. c. m. dec.of m. 14 .25 .6 12 .2 .6 .4 147 .6 .3 .4 121 .7 .6 .5 .3 .25 13 .14 .4 10 .8 .7 .3 121 .7 .5 .4 324 .6 .5 .4 .5 .75 13 .12 .3 15 .7 .6 .4 134 .3 .4 .6 242 .5 .6 .0 .4 .25 15 .10 .2 16 .4 .3 .2 147 .6 .5 .4 221 .3 .4 .5 .6 .50

55 .62 .5 55 .3 .3 .3 551 .3 .8 .8 910 .3 .2 .5 .9 .75

16. Add 278D. 9d. 7c. 4m. .21+87D. 6d. 9c. 5m. .75+ 396D. 4d. 7c. 6m. .25+464D. 6d. 3c. 5m. .35, together.

Ans. 1227D. 7d. 8c. 1m. .56.

17. A gentleman has the following charges entered in his ledger: A. 420D. 27c. 5m.; B. 671D. 87c. 6m.; C. 742D. 33c. 4m.; D. 621D. 25c. 7m.; E. 520D. 47c. 6m.; required the amount. Ans. 2976D. 21c. 8m. 18. A farmer sold his wheat for 1724D. 87c. 5m.; rye, 1296D. 18c. .75; corn, 964D. 25c. 8m.; oats, 250D. 37c. 5m. ; required the amount of the value of his produce.

Ans. 4235D. 69c. .55. 19. A drover paid for his drove as follows: oxen, 1800D. 75c.; cows, 878D. 50c.; sheep, 502D. 31c.; he also purchased 2 horses for 75D. 50c. each; required the cost of his drove. Ans. 3332D. 56c. 20. Add 420E. 8D. 27c. 6m. .75+371E. 8D. 29c. 4m. .25 +781E. 5D. 17c. .8m. 37+416E. 7D. 14c. 5m. .50, together. Ans. 1990E. 8D. 89c. 4m. .87

SUBTRACTION OF DECIMALS.

RULE.

1. Write down the numbers the same as in Simple Subtraction, observing that the decimal points stand directly under each other. 2. Then subtract in the same way as in whole numbers and place the decimal point in the remainder under those above it. Proof as Simple Subtraction.