EXAMPLES FOR PRACTICE.

Find the value of the following in decimals:

1.录;是;急;;;

193. Sometimes (as in Example 7 and 14 above) no decimal can be obtained exactly equivalent to a common fraction. This is because the division does not terminate, but the same figure or set of figures keeps recurring in the quotient. In such cases, the further the division is carried out, the more nearly correct will the answer be.

The

194. A decimal in which one or more figures are constantly repeated, is called a Circulating Decimal. repeated figure or figures are called the Repetend.

195. A repetend is denoted by a dot placed over it, if it is a single figure, or over its first and last figure, if it contains more than one. Thus: .3 .333, &c. .454545, &c. .2148 = .2148148, &c.

.45 =

196. A Pure Circulating Decimal is one that consists wholly of a repetend; as, .3, .243.

A Mixed Circulating Decimal is one in which the repetend is preceded by one or more decimal figures, which form what is called the Finite Part: as, .23; .2 is the finite part.

198. Why, in some cases, can not a decimal be obtained equivalent to a common fraction?-194. What is a Circulating Decimal? What are the repeated figure or figures called?-195. How is a repetend denoted?-196. What is a Pure Circulating Decimal? What is a Mixed Circulating Decimal? Give examples.

197. REDUCTION OF CIRCULATING DECIMALS.-Reducing according to the rule in § 192, we find

It will be seen from the above that the denominator of a repetend consists of as many nines as it contains figures. Hence the following rule:

198. RULE I.-To reduce a repetend to a common fraction, write under it for a denominator as many nines as it contains figures.

199. RULE II.-To reduce a mixed circulating decimal, reduce the repetend to a common fraction, as above, annex it to the finite part, and place the whole over the denominator of the finite part. Reduce the complex fraction thus formed to a simple one.

EXAMPLE. Reduce .2336 to a common fraction.

Reduce 36 to a common fraction:

Annex the fraction to the finite part:

.23

28

Place the whole over the denom. of the finite part:

100

1. Write as circulating decimals: .3333+ (.3); .263263263+ (.263); .10471047+; .246666+ (.246); .1492121+; 4.9871871+; 3.2300300+; .12345671234567+; .2424+.

197. Of what does the denominator of a repetend consist? How is this shown? -198. Recite the rule for reducing a repetend to a common fraction.-199. Recite the rule for reducing a mixed circulating decimal to a common fraction. Apply this rule in the given example.

2. Write as circulating decimals (§ 197): 3 (.7); 3 (.07); ‚ða

(.007); 有a; aobao; bt; 有a; obiba; audosos; &; doi đổði

81 9999

3. Reduce to common fractions (3198) in their lowest terms: Ans. &; Th; 111; 9999.

.25; .081; .315; .i000.

35

1000

4. Reduce to common fractions (199) in their lowest terms: .06; .243; .63219; .81003.

Ans.

5. How much more is .8 than .8?
6. How much more is .21 than .21?

7. How much less is .72 than .72?

8. Which is the greater, .48 or .48, and how much?

Ans. .

Ans. 3300.

13. Reduce .12 and .1894.

Ans. 1¦}.
Ans. 15.
Ans. ggg.

76

14. Reduce .083 and .4896. 15. Reduce .135 and .0398. 16. Reduce .135 and .6345.

CHAPTER XII.

FEDERAL MONEY.

200. A Coin is a stamped piece of metal used as money. 201. By the Currency of a country is meant its money, consisting of coins, bank bills, government notes, &c.

202. Different countries have different currencies. The currency of the United States is called Federal Money.

TABLE OF FEDERAL MONEY.

10 mills (m.) make 1 cent,

10 cents,

10 dimes,

10 dollars,

200. What is a Coin?-201. What is meant by the Currency of a country?—202. What is the currency of the United States called? Recite the Table of Federal Money.

The mill, one thousandth part of a dollar, takes its name from the Latin word mille, a thousand; the cent, one hundredth of a dollar, from the Latin centum, a hundred; the dime, one tenth of a dollar, from the French dime, a tithe or tenth. The word dollar comes from the German thaler. The dollar-mark is supposed to have originated from the letters U. S. (for United States) written one upon the other.

203. UNITED STATES COINS.-The coins of the United States represent all the denominations of the above Table except mills, as well as other values. They are as fol

lows:

The gold and silver coins are nine tenths pure metal, the former being alloyed with one tenth of silver and copper, and the latter with one tenth of copper. The copper coins consist of 88 parts of copper to 12 of nickel.

204. WRITING AND READING FEDERAL MONEY.-In passing from mills to cents, from cents to dimes, and from dimes to dollars, we go each time to a denomination ten times greater, just as we do in passing from thousandths to hundredths, from hundredths to tenths. Federal Money is therefore a decimal currency, and may be written and operated on in all respects like decimals.

205. In writing and reading Federal Money, the only denominations used are dollars, cents, and mills. The dollar is the unit or integer, and is separated by the deci

From what does the mill take its name? The cent? The dime? The dollar? How is the dollar-mark supposed to have originated?-203. Name the gold coins of the United States, and their value. The silver coins. The copper coins. What proportion of the gold and silver coins is pure metal? With what are they alloyed? Of what do the copper coins consist ?-204. What kind of a currency is Federal Money? How may it be written and operated on?-205. What denominations are used in writing and reading Federal Money? Which of these is the integer? How is it separated from cents?

mal point from cents, which occupy the first two places on the right of the point, mills occupying the third. Hence the rules.

Cents occupy two places,-that of dimes and their own,-because we do not recognize dimes in reading. Cents are sometimes written in the form of a common fraction, as hundredths of a dollar; as, $52.

206. RULE I.-Write Federal Money decimally, the dollars as integer, the cents as hundredths, the mills as thousandths.

207. RULE II.-In reading Federal Money, call the integer dollars, the hundredths cents, the thousandths mills.

1. Write eleven dollars, eleven cents.

2. Write six hundred dollars, three mills.

3. Write ninety-eight dollars, seven cents.

4. Write one thousand dollars, ten cents, nine mills.

5. Write six dollars, seventeen cents, eight mills.

6. Write ninety-nine cents, nine mills.

7. Write a million dollars, one cent, one mill.

208. OPERATIONS IN FEDERAL MONEY.-To add, subtract, multiply, or divide Federal Money, express the given amounts decimally, and proceed as in decimals.

Represent cent as 5 mills, cent as 25 ten thousandths of a dollar. Thus: 37 cents = $.375 64 cents = $.0625

How many places do cents occupy? Why? How are cents sometimes written? -206. Recite the rule for writing Federal Money.-207. Recite the rule for reading Federal Money.-208. Give the rule for adding, subtracting, multiplying, or dividing Federal Money. How iscent represented? cent?