figure one place to the left or the decimal point one place to the right, we multiply 3.7267 by 10 by moving the decimal point one place to the right.

By the same process of reasoning we multiply by 100 by removing the decimal point two places to the right, etc., etc.

17. What cost 17.35 tons of hay at $17.375 per ton?

18. What cost 13.75 dozen eggs at $.1875 per dozen? 19. What cost 18.75 pounds of butter at $.1875 per pound?

20. Multiply three hundred and three thousand one hundred forty-one ten-thousandths by twenty-four and three thousand five hundred sixty-one hundred-thousandths.

9.8 rods?

Ans. 7218.232585101. 21. There are 16.5 feet in 1 rod. How many feet in Ans. 161.7 ft. 22. There are 5.5 yards in 1 rod. How many yards in 80 rods? Ans. 440 yards.

What

23. Bought 143.5 acres of land at $75.25 per acre. did the whole cost? Ans. $10798.375. 24. What is the product of 1.25 multiplied by 800? 25. What cost 4000.7 bushels corn at $.75 a bushel?

Ans. 18.1.

30. (4.5 x 1.8) + (12.5 x .8)=?

31. (9.2.52) x (123-114.32) = ?

32. (683.21+316.79999.83) x .17?

Ans. 75.3424.

Ans. .0289.

3 hundredths are contained in 6 hundredths 2 times.

3 thousandths are contained in 6 thousandths 2 times. Hence,

133. When the divisor and dividend are like numbers, or are of the same order of units, the quotient is ones.

EXAMPLE.-Divide 37.18 by 1.43.

134. The dividend must contain at least as many deci

mal figures as the divisor.

One-half of 6 hundredths is 3 hundredths: .06÷3.02.

One-half of 6 thousandths is 3 thousandths.

3).006

.002

135. When the divisor is an integer, the quotient will be of the same orders of units as the dividend.

EXAMPLE.-Divide .4375 by 35.

3. Divide .0425 by 25.

DIVISION.

4. Divide .00144 by 12.

5. Divide 1728.12 by 12.

Ans. .0017.

Ans. .00012.

Ans. 144.01.

136. The quotient contains as many decimal figures as the number of those in the dividend exceeds those in the

divisor.

EXAMPLE.-Divide 4.6875 by 3.125.

SOLUTION.

3.125) 4.6875 ( 1.5 3 125

1 5625

1 5625

EXPLANATION.-The right-hand figure of the divisor is thousandths, and the corresponding order of the dividend is 7 (thousandths). Hence, the quotient of 4.687 divided by 3.125 is an integer (133).

Placing the decimal point after the quotient figure, 1, and completing the division, the quotient obtained is 1.5, which contains one decimal place (136).

The dotted vertical line in the solution shows what figures of the dividend are used to obtain the integral part of the quotient.

When decimal ciphers are annexed to form partial dividends, they are counted as decimal figures of the dividend.

137. The right-hand figure of any remainder after division is always of the same order of units as the last figure of the dividend used to obtain it.

1. Into how many building lots, each containing .48 of an acre, can 8 acres of land be divided?

Ans. 16 lots, and .32 of an acre left.

2. How many ice-pitchers, each weighing 2.13 pounds, can a manufacturer make from 15 pounds of silver?

Ans. 7 pitchers, with .09 of a pound left.

138. RULE.-Divide as in whole numbers, and point off from the right of the quotient as many places for decimals as the number of decimal places in the dividend exceed the number in the divisor.

If there are not so many places in the quotient, supply the deficiency by prefixing ciphers.

If in the course of division ciphers have been annexed to the dividend, regard each cipher annexed as a decimal place.

PROBLEMS.

1. Divide by 10.

2. Divide .875 by 100.

Ans. .07.

Ans. .00875.