6. It took 61 yards of cloth at $3 per yard for Elsie's dress, and 114 yards at $ per yard for her mother's. How much less did the cloth for Elsie's dress cost than for her mother's?

7. A boy bought 90 cocoanuts at $1 per dozen, and sold them at $1 apiece. How much money did he gain?

8. A grocer bought a bunch of bananas for $14. He sold 3 dozen from the top at $3 per dozen, and the rest, 61 dozen, at $1 per dozen. How much did he gain?

9. If a

224-pound bag of salt costs $13, how much will a 56-pound bag cost at the same rate?

10. When 16 pounds of salt cost $16, how many pounds are there in a bag that costs $13?

11. The cost of oiling a stretch of highway in Pennsylvania was $65,000, of which the state paid $43,333. What part of the cost was paid by the state?

12. Mr. Thayer owned & of a section of land. He sold § of his land to Mr. Hall, who gave of his part to a son. What part of the whole section did Mr. Hall's son receive? How many acres? 13. In constructing 9 miles of railroad track 2640 ties were used per

mile. Find the whole number of ties used and their cost at $4 each.

14. If 571 bushels of seed are required for a rice field of 241 acres in South Carolina, and § of a bushel for of an acre in Japan, how much seed is required per acre in each place? how much more per acre in South Carolina than in Japan?

15. A grain elevator had a bin 7 ft. square and 80 ft. deep. How many bushels did it hold, allowing 11 cu. ft. to the

bushel?

16. One side of a tight board fence 45 yd. long and 17 yd. high was painted two coats. It took 183 lb. of paint for the first coat and 131 lb. for the second. How many square yards did a pound of paint cover for the first coat? for the second?

DECIMAL FRACTIONS

Notation and Numeration of Decimals

258. The orders of decimals below thousandths are tenthousandths, hundred-thousandths, millionths, etc., as shown in the following table.

The orders below millionths are ten-millionths, hundred-millionths, billionths, ten-billionths, etc. They are seldom used.

1. 365.743298 is read "365 and 743,298 millionths." 40.0024 is read "40 and 24 ten-thousandths.'

88.30696. is read "88 and 30,696 hundred-thousandths.'

2. What decimal place is occupied by

Hundred-thousandths?
Hundred-millionths?

3. How many decimal figures are required to express thousandths? ten-thousandths? hundred-thousandths? millionths? ten-millionths? hundred-millionths?

4. 1, .1, .01, .001, .0001, .00001, .000001.

What part is each decimal of the number on its left?
How many tenths are there in 1? hundredths in .1? etc.

In the Arabic or decimal system of notation, a unit of any order is of the next higher or left-hand unit, and 10 times the next lower or right-hand unit.

In reading a decimal, it should be read as an integer, and the denomination of the right-hand figure should be added.

In reading a mixed decimal the word "and" is used between the integral and decimal parts, and not elsewhere.

260. Express in figures:

1. 2 hundreds and 25 thousandths.

2. 20 units and 733 thousandths.

3. 625 units and 85 ten-thousandths.

4. 16 thousands, 382 units, and 95 millionths.

5. 485 millions, 7 thousands, and 17 thousandths.

6. 1 million, 1 thousand, 1 unit, and 1 hundred-thousandth.

7. Seventy-five and twenty-one thousandths.

8. Ten and three thousand one hundred six millionths.

9. Ninety-six and four hundred ninety ten-thousandths.

10. Six hundred sixty-six thousand six hundred sixty-six millionths.

11. Six hundred sixty-six thousand and six hundred sixtysix millionths.

12. Four hundred seventeen thousand two hundred six millionths.

13. Four hundred seventy-seven thousand and two hundred sixty-nine millionths.

14. Ninety-six and thirty-two ten-thousandths.

15. Two hundred sixty and three hundred fifteen hundredthousandths.

262. Reduction of common fractions to decimals.

WRITTEN EXERCISES

1. Reduce to a six-place decimal.

7)4.000000 .571429

=

of 5 tenths or of 50 hundredths 7 hundredths and 1 hundredth remaining; and so on. The last division gives of 60 millionths = 84 millionths. Since 84 millionths is nearer 9 millionths than 8 millionths, 9 is written in the quotient rather than 8; but a small minus sign is written after the 9 to show that the true quotient is a little less than .571429.

In the following, no results need be carried beyond six decimal places.

The small plus signs show that the true quotients are a little larger than those set down, but less than millionth larger.

After finding the first three figures of the quotient by long division, it is found that the new dividend is like the original dividend. Hence, the next three figures of the quotient will be like the first three; and in fact the same set of figures will recur, however far the division is carried.

The short division process is advised when the divisor can be separated readily into factors.