Remove the decimal point as many places to the right as there are ciphers in the multiplier.

NOTE.-If there be not enough decimal places in the product, supply the deficiency by annexing ciphers.

LESSON VI.

Division of Decimals.

1. How many times are 2 tenths contained in 8 tenths? 3 tenths in 9 tenths?

2. How many times are 4 hundredths contained in 12 hundredths? 6 hundredths in 42 hundredths? 3. How much is 8 = ? 9 tenths ÷ 3 tenths?

10

4. How much is .06 .02? .56.07?

5. Of what order is the quotient when tenths are divided by tenths? Hundredths by hundredths? 6. Of what order is the quotient when any number is divided by a like number?

PROCESS.

34.5 10: = 3.45.

34.5

100=.345.

By .079.
By 168.
By $2.07.
By .096.

By annexing two decimal ciphers to 62.5, the dividend and divisor are made like numbers, and hence their quotient is an integer.

By .16.
By .0125.

By .0302.
By .00035.

By .0175.
By 100.

The removal of the decimal point one order to the left, removes each figure in 34.5 one order to the right, and hence

divides its value by 10; and the removal of the decimal point two places to the left divides it by 100.

23. Divide 436.7 by 100. By 1000.
24. Divide 234.6 by 1000. By 100000.

PRINCIPLES AND RULES.

Art. 99. PRINCIPLES.-1. The dividend contains as many decimal places as both divisor and quotient.

2. The quotient contains as many decimal places as the number of decimal places in the dividend exceeds the number in the divisor.

3. Each removal of the decimal point one place to the left divides a decimal by 10.

Art. 100. RULES.-1. To divide one decimal by another, Divide as in the division of integers, and point off as many decimal places in the quotient as the number of decimal places in the dividend exceeds the number in the divisor.

NOTES.-1. When the divisor contains more decimal places than the dividend, supply the deficiency in the dividend by annexing decimal ciphers.

2. When the quotient has not enough decimal figures, supply the deficiency by prefixing decimal ciphers.

3. When there is a remainder, the division may be continued by annexing ciphers, each cipher thus annexed adding one decimal place to the dividend. Sufficient accuracy is usually secured by carrying the division to three decimal places.

2. To divide a decimal by 10, 100, 1000, etc., Remove the decimal point as many places to the left as there are ciphers in the divisor.

REVIEW PROBLEMS.

1. Express decimally of one hundredth.

2. Reduce to a decimal.

3. Change .0325 to a common fraction.

4. Divide 84.564 by 9.72.

5. Divide 36.72 by 3.6. By .036.

6. Divide 25.6 .56 by

7. Divide 348.6 by 100.

8. Divide 17.28 by 24.

.0128.

By 2000.

By 2400.

9. Multiply 27.5.025 by 76.8 ÷ .48.

10. What will be the cost of excavating 437.24 cubic yards of earth at $1.65 a cubic yard?

Art. 101. United States Money is the legal currency of the United States. It is also called Federal Money.

The denominations are mills, cents, dimes, and dollars.

NOTES.-1. United States money consists of Coin and Paper Money. Coin is called Specie Currency, or Specie, and paper money is called Paper Currency.

2. The principal gold coins are the double eagle ($20), eagle ($10), half-eagle ($5), quarter-eagle ($21), three-dollar piece, and dollar.

The silver coins are the dollar, half-dollar, quarter-dollar, and dime. The smaller coins are the five-cent piece, three-cent piece, two-cent piece, and cent. The five-cent piece and the three-cent piece are made of copper and nickel, and the two-cent piece and cent are made of bronze, an alloy of copper, tin, and zinc.

3. Paper money consists of notes issued by the United States, called Treasury Notes, and bank notes issued by banks.

1. How many mills in 1 cent?
7 cents? 9 cents?

4 cents?

2. How

many cents in 1 dime?

5 dimes?

8 dimes? 10 dimes?

In 5 cents?

In 4 dimes?

3. How many dimes in 1 dollar? In 3 dollars? 6 dollars? 4 dollars? 8 dollars?

4. How many cents in 10 mills?

40 mills? 60 mills? 80 mills?

In 50 mills?

5. How many dimes in 40 cents? In 90 cents? 60 cents? 70 cents? 100 cents?

6. How many dollars in 50 dimes? In 70 dimes? 60 dimes? 80 dimes? 100 dimes?

7. How many dimes in 25 cents? In 75 cents? 15 cents? 35 cents? 95 cents?

8. How many cents in 35 mills? In 65 mills? 25 mills? 75 mills? 95 mills?

9. How many cents in 5 dimes? In 15 dimes? 45 dimes? 30 dimes?

10. How many dimes in 15 cents? In 95 cents? 85 cents? 65 cents?

11. How many cents in 1 dollar? In 5 dollars? 7 dollars? 9 dollars? 8 dollars?

12. How many dollars in 200 cents? In 500 cents? 400 cents? 900 cents?