Eagles are expressed in dollars, and dimes in cents.— Thus, instead of 5 eagles, we say, 50 dollars; instead of 7 eagles and 5 dollars, we say, 75 dollars, &c. So, instead of 6 dimes, we say, 60 cents; instead of 8 dimes and 7 cents, we say, 87 cents, &c.

205. It will be seen from the table, that the denominations of Federal Money increase and decrease in value from right to left and left to right, in a tenfold ratio; and that it is expressed, like simple numbers, by the Decimal or Arabic Notation.

206. The Dollar is regarded as the unit; cents and mills are fractional parts of the dollar, and are distinguished from it by a decimal point or separatrix (.) in the same manner as common decimals. (Art 179.) Dollars therefore occupy units' place of simple numbers; eagles or tens of dollars, tens' place, &c. Dimes, or tenths of a dollar, occupy the place of tenths in decimals; cents, or hundredths of a dollar, the place of hundredths; mills, or thousandths of a dollar, the place of thousandths; tenths of a mill, or ten thousandths of a dollar, the place of ten thousandths, &c.

OBS. 1. Since dimes in business transactions are expressed in cents, two places of decimals are assigned to cents. If therefore the number of cents is less than 10, a cipher must always he placed on the left hand of them; for cents are hundredths of a dollar, and hundredths occupy the second decimal place. (Art. 181.) For example, 4 cents are written thus .04; 7 cents thus .07; 9 cents thus .09, &c.

2. Mills occupy the third place of decimals; for they are thousandths of a dollar. Hence, when there are no cents in the given sum, two ciphers must be placed before the mills.

207. Hence, to read any sum of Federal Money. Call all the figures on the left of the decimal point dollars; the first two figures after the point, are cents; the

205. How do the denominations of Federal Money increase and decrease? How is it expressed? 206. What is regarded as the unit in Federal Money? What are cents and mills? How are they digtinguished from dollars? 207. How do you read Federal Money? Obs. What other Inode of reading Federal Money is mentioned?

third figure denotes mills; the other places on the right are decimals of a mill. Thus, $3.25232 is read, 3 dollars, 25 cents, 2 mills, and 32 hundredths of a mill.

OBS. Sometimes all the figures after the point are read as decimals of a dollar. Thus, $5.356 is read, "5 and 356 thousandths dollars."

Read the following sums of Federal Money:

6. 201 dollars and 9 cents.

7. 300 dollars, 5 cents, and 3 mills.

8. 4 dollars, 6 cents, and 8 mills.

9. 100 dollars, 7 cents, 5 mills, and 3 tenths of a mill. 10. 1000 dollars, 6 mills, and 36 hundredths of a mill.

Note. In business transactions, when dollars and cents are expressed together, the cents are frequently written in the form of a common fraction. Thus, $76.45 are written 76100 dollars.

45

REDUCTION OF FEDERAL MONEY.

CASE I.

Ex. 1. How many cents are there in 75 dollars?

Suggestion. Since in 1 dollar there are 100 cents, in

75 dollars there are 75 times as many.

7500.

And 75 x 100= Ans. 7500 cents.

Ans. 90 mills.

2. In 9 cents, how many mills? 3. In 25 dollars, how many mills? Ans. 25000 mills.

Note. To multiply by 10, 100, &c., is simply annexing as many ciphers to the multiplicand, as there are ciphers in the multiplier. (Art. 59.) Hence,

208. To reduce dollars to cents, annex two ciphers.

To reduce dollars to mills, annex three ciphers.
To reduce cents to mills, annex one cipher.

OBS. To reduce dollars and cents to cents, erase the sign of dollars and the separatrix. Thus, $25.36 reduced to cents, becomes 2536

cents.

4. In $5, how many cents?
5. How many mills in $364?
6. How many mills in $621?
7. How many cents in $6245?
8. Reduce $75.26 to cents.
9. Reduce $625.48 to cents.

CASE II.

10. In 4500 cents, how many dollars?

Suggestion. Since 100 cents make 1 dollar, 4500 cents will make as many dollars as 100 is contained times in 4500. And 4500-100=45. Ans. $45.

11. In 150 mills, how many cents? Ans. 15 cents. 12. In 25000 mills, how many dollars? Ans. $25.

Note. To divide by 10, 100, &c., is simply cutting off as many figures from the right of the dividend as there are ciphers in the divisor. (Art. 80.) Hence,

209. To reduce cents to dollars, cut off two figures on the right.

To reduce mills to dollars, cut off three figures on the right.

To reduce mills to cents, cut off one figure on the right.

OBS. The figures cut off are cents and mills.

QUEST.-208. How are dollars reduced to cents? Dollars to mills? Cents to mills? Obs. Dollars and cents to cents? 209. How are cents reduced to dollars? Mills to dollars? Mills to cents? Obs. What are the figures cut off?

13. In 325 cents, how many dollars? Ans. $3.25. 14. In 423 mills, how many cents? Ans. 42c. 3m. 15. In 4320 mills, how many dollars?

16. How many dollars in 63500 cents? 17. How many cents in 4890 mills?

210. Since Federal Money is expressed according to the decimal system of notation, it is evident that it may be subjected to the same operations and treated in the same manner as decimal fractions.

ADDITION OF FEDERAL MONEY.

Ex. 1. A man bought a cow for $15.75, a calf for $2.375, a sheep for $3.875, and a load of hay for $8.68: how much did he pay for all?

Operation.

15.75

2.375

3.875 8.68

$30.680 Ans.

We write the dollars under dollars, cents under cents, &c. Then add each column separately, and point off as many figures for cents and mills, in the amount, as there are places of cents and mills in either of the given numbers.

211. Hence, we derive the following

GENERAL RULE.

Write dollars under dollars, cents under cents, &c., so that the same orders or denominations may stand under each other. Add each column separately, and point off the amount as in addition of decimal fractions. (Art. 187.)

OBS. If either of the given numbers have no cents expressed, it is customary to supply their place by ciphers.

2. A farmer sold a firkin of butter for $9.28, a cheese for $1.17, a quarter of veal for 56 cents, and a bushel of wheat for $1.12: how much did he receive for the whole ?

QUEST.-211. How is Federal Money added? How point off the amount? Obs. When any of the given numbers have no cents expressed, how is their place supplied?

3. A man bought a hat for $5.375, a cloak for $35.68, and a pair of boots for $4.75: how much did he pay for all? 4. What is the sum of $37.565, $85.20, $90.03, and $150.638?

5. What is the sum of $10.385, $46.238, $190.62, and $23.036 ?

6. What is the sum of $23.005, $16.03, $110.738, and $131.26 ?

7. What is the sum of 63 dolls. and 4 cts., 86 dolls. and 10 cts., and 47 dolls. and 37 cts.?

8. What is the sum of $608.05, $365.205, $2.268, and $47.006 ?

9. What is the amount of 11 dolls. 3 cts. and 5 mills, 16 dolls. and 8 mills, 49 dolls. 7 cts. and 8 mills?

10. What is the amount of 100 dolls. and 61 cts., 51 dolls. and 3 cts., 65 dolls. 8 cts. and 3 mills?

11. What is the amount of 95 dolls. 67 cts. and 8 mills, 120 dolls. 45 cts., 101 dolls. 7 cts. and 9 mills?

12. A lady bought a bonnet for $6.67, a pair of gloves for $0.625, a pair of shell combs for $0.75, and a cap for $2.50 what was the amount of her bill?

SUBTRACTION OF FEDERAL MONEY.

Ex 1. A man bought a horse for $56.50, and a cow for $23.38: how much more did he pay for his horse than his cow?

Operation.

$56.50

23.38

$33.12 Ans.

We write the less number under the greater, placing dollars under dollars, &c., then subtract, and point off the answer as in subtraction of decimals.

212. Hence, we derive the following

GENERAL RULE.

Write the less number under the greater, with dollars under dollars, cents under cents, &c., then subtract, and point off the remainder as in subtraction of decimal fractions. (Art. 189.)