21. .075.by 481.

22. 2.42 by 50.

23. .0075 by 2.8.

24. 43.6 by .073.

25. Multiply 24 thousandths by 61 hundredths.

26. Multiply 4.35 by 10. By 100.

PROCESS.

4.35 X 10

43.5, Ans. 4.35 X 100 435, Ans.

==

Since the value of decimal orders increases from right to left

tenfold (Art. 130, Pr. 2), the removal of the decimal point one

place to the right removes each figure one order to the left, and hence multiplies 4.35 by 10. The removal of the decimal point two places to the right multiplies 4.35 by 100. 27. Multiply 4.085 by 100. By 1000. 28. Multiply 3.0048 by 1000. By 100000.

PRINCIPLES AND RULES.

Art. 137. PRINCIPLES.-1. The number of decimal places in the product equals the number of decimal places in both factors.

2. Each removal of the decimal point one place to the right, multiplies a decimal by 10.

Art. 138. RULES.-1. To multiply one decimal by another, Multiply as in the multiplication of integers, and point off as many decimal places in the product as there are decimal places in both multiplicand and multiplier.

NOTE. If there be not enough decimal figures in the product, supply the deficiency by prefixing decimal ciphers.

2. To multiply a decimal by 10, 100, 1000, etc., 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?

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?

WRITTEN EXERCISES.

7. Divide 6.25 by by .25.

14. Divide $17.595 by $.85. By $2.07.
15. Divide .0768 by 9.6. By .096.
16. Divide 62.5 by .025.

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

PRINCIPLES AND RULES.

Art. 139. 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. 140. 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.

8

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 .0128.

7. Divide 348.6 by 100.

By 2000.

8. Divide 17.28 by 24. 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?

SUGGESTION.-"Once," "2 times,' "3 times," "4 times," etc., found in the left-hand column, are to be supplied in each of the other columns.