CHAPTER VI.

DECIMAL FRACTIONS.

ART. 133. A DECIMAL FRACTION is one in which the denominator is not expressed, but is understood to be a unit followed by one or more ciphers; or such a fraction the successive orders of which increase from right to left in a tenfold ratio, consequently decrease from left to right in the same ratio.

Decimal Fractions originate from dividing 1 into 10 equal parts; each of these parts into 10 other equal parts; and each of the parts thus obtained into 10 other equal parts, and so on, indefinitely. Thus, 110=;÷÷ 10 = Too; Too ÷ 10 Too, &c., which are expressed in Decimals as follows :

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ART. 134. In expressing DECIMAL FRACTIONS, the numerator only is written with a point before it, called a Decimal point or Separatrix, to distinguish it from whole numbers; the denominator being understood. Thus,

By inspecting the above fractions, it is observed that tenths occupy the first place at the right of the decimal point; that hundredths occupy the second place; that thousandths occupy the third place, &c.

We also observe that each removal of a figure one place towards the right, decreases its value in a tenfold ratio. Hence,

Every cipher placed on the left of a decimal figure diminishes its value in a tenfold ratio. Thus, 9 = ; 09

; and 009 = o, &c.

If a cipher be placed on the right of a decimal figure, it does not change its value, as the figure still occupies the same place. Thus, 9 ·90 900, 1% 900 &c.

10001

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NUMERATION OF DECIMAL FRACTIONS.

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10

ART. 135. A whole number and a decimal fraction, when considered together, is called a mixed number; the relation and names of which can be learned from the following

ART. 136. To read a Decimal number expressed in figures.

Read the figures as in whole numbers, and add the name of the decimal place. Thus, 9 is read nine-tenths; 09 is read nine hundredths; 100024 is read one hundred thousand and 24 millionths, &c

REMARK.-To ascertain the name of the right hand figure, begin at the left and name each figure till you come to the last one, which will be the name required.

UNITED STATES CURRENCY,* OR FEDERAL MONEY. ART. 137. United States Currency is the legal Money of the United States, and is expressed according to the Decimal Scale of notation.

Money may be considered the measure of the value of things.

The denominations of the United States Currency are Eagles, Dollars, Dimes, Cents, and Mills.

The coins of the United States are the

NOTE.-By an act of Congress, January 18th, 1837, the gold and silver coin must consist of pure metal, and alloy.

REMARK. This currency is usually called Federal Money, because it was made the currency of the United States at the time of the adoption of the Federal Constitution, August 8th, 1786.

The word Dollar is derived from a Danish word, which was derived from Dale, the name of the town in which this coin was first made. The word Dime is derived from a French word signifying ten;-the word Cent, from a Latin word signifying one hundred ;-the word Mill, from a Latin word signi fying one thousand. The terms, Dime, Cent, and Mill, are applied to coins of our currency, in consequence of the relation they respectively bear to the DOLLAR,

The alloy for gold must consist of an equal quantity of silver and copper, and the alloy for silver of pure copper.

The three-cent piece is silver and copper.

Before 1837, the gold for coinage consisted of 22 pure gold, silver, and copper; or, as sometimes expressed, 22 carats gold, 1 of silver, and 1 of copper; the word carat meaning one twenty-fourth.

Silver for coinage consisted of 1489 parts of pure silver, and 179 parts of pure copper; or, expressed in carats, of silver, and 2% of copper.

21

E.

ART. 138. The accounts of the United States are kept in Dollars Cents, and Mills. In business transactions, the eagle is expressed in dollars, the dime in cents. Thus, 4 eagles, according to the preceding table, is = 40 dollars; and, instead of saying 4 eagles and 5 dollars, we say 45 dollars. Also, 7 dimes are 70 cents; therefore, instead of saying 7 dimes and 9 cents, we say 79 cents, &c.

ART. 139. In the United States Currency, dollars are Integers, and therefore, occupy the place of units. Cents express hundredths of a dollar, consequently they occupy the first and second place on the right of the decimal point; the third place is mills; &c. Thus, $47.356, is read forty-seven dollars thirty-five cents and six mills.

ART. 140. To express any number of cents less than 10, there should be a cipher placed between them and the decimal point, as cents are hundredths of a dollar, and therefore occupy two places; if mills only are expressed,

This symbol is probably a contraction of the letter U, placed upon an 8, to denote U. S. (United States.)

ART. 142.] REDUCTION OF DECIMALS TO COMMON FRACTIONS. 123

two ciphers should be placed between them and the decimal point. Thus:

4 cents is written $.04, and is read 4 hundredths of a dollar. 12 cents is written $12, and is read 12 hundredths of a dollar. of a cent is written $.003, and is read 3 of 1 hundredths of a dollar. 5 mills is written $.005, and is read 5 thousandths of a dollar. 4 cents and 6 mills is written $.046, and is read 46 thousandths of a dollar.

ART. 141. It might be well to observe, that the first figure after the decimal point, expresses tenths of a dollar, or tens of cents; the second, cents; the first two places taken together express hundredths of a dollar, or cents; the third mills; the fourth tenths of mills, &c.

REDUCTION OF DECIMALS TO COMMON FRACTIONS.

ART. 142. From what has been said of Decimal Fractions, we infer that a decimal can be reduced to a common fraction by erasing the decimal point, and underneath writing the denominator, which is a unit followed by as many ciphers as there are places in the decimal; then reduce the fraction to its lowest terms.

1. Reduce 025 to a common fraction.

Reduce each of the following decimals of a dollar to equivalent common fractions.

11. Express 6.0625 by an integer and a common fraction.

12. Express 12.25 by an integer and a common fraction 13. Express 14.5 by an integer and a common fraction 14. Express 25.625 by an integer and a common frac tion.

15. Express 45.875 by an integer and a common frac tion.