11. The batting average of a baseball player is found by dividing the number of hits that he makes by the number of times he is at bat. The records made up to August in a certain year by certain of the best batters in the American and National Leagues are here given. Find the batting average of each, correct to .001.

12. Forty-two acres of a farm of 160 acres are woodland. What part is woodland? Find the answer correct to .001.

13. On October 16, 1916, the national debt of the United States was estimated to be $12 per capita, that is, $12 for each person; that of Great Britain, $376 per capita; of France, $360; and of Germany, $290. The per capita debt of each of the other countries was how many times that of the United States? Answer correct to .01.

14. Light travels in waves. The length of a wave of a certain kind of light is .0000154 in. How many such waves in a ray of this light 1 yd. long? Find result to the nearest unit.

15. A certain bacterium is .00001 in. long. How many such bacteria can be placed in a row an inch long?

16. A one-inch cube of metal is heated until its edges are each 1.003 in. Find its volume correct to the nearest .001 cu, in. Find its total surface correct to .001 sq. in.

17. Some ladies' suits are marked at the following prices: $50; $45.50; $35; $26.50; $34.50; $15.75; $32.25; $38; $18; $20.50; $27.25; $31.50. At a clearance sale they are all marked at the same price, which is of their average price, to the nearest 25¢. Find the sale price.

19. A match is .1 in. square on the end and 21 in. long. Find the volume of 10,000 matches.

Find the following quotients:

35. The circumference of a circle is 3.1416 times the diameter. In a piece of machinery it is desired to have the circumference of a wheel exactly 10 ft. Find the diameter correct to .01 in.

36. The diagonal of a square is 1.4142 times the side. Find the diagonal of a field which is 40 rods square, correct to .01 of a rod.

37. Twelve measurements of the diameter of a steel wire gave the following fractions of an inch : .061, .062, .064, .060, .061, .065, .059, .066, .058, .062, .060, .064. Find the average of these measurements to the nearest .001 in.

THE METRIC SYSTEM

26. Advantages of the Metric System. The table of United States money is more easily learned than the table of linear measure because throughout the table of United States money the same number of units of any order makes one of the next higher.

In making the table of United States money 10 units of one order were taken to make one of the next higher, just as in ordinary numbers. This makes reduction from one denomination to another very simple. Thus, cents are reduced to a fraction of a dollar by dividing by 100, and may be written as a decimal. United States money and ordinary numbers are said to be written on a scale of 10, or on a decimal scale.

In computing weights and measures much time and labor are saved when all the tables are written on the scale of 10. Such a system of measures was devised by the French Government and is called the Metric System.

The convenience of the Metric System has led to its general adoption in Central and South America and in Europe except in Great Britain. It is used in science throughout the world. Its use in the United States would greatly simplify the learning and use of tables of weights and measures. The increased use of the Metric System in our foreign trade and the frequent use of metric units in articles in newspapers and magazines make it necessary for all Americans to become familiar with this system and its uses.

27. Linear measure. The meter is the primary unit of length of the metric system. All other units are based upon the meter. The meter was computed to be one ten-millionth of the distance from the equator to the pole. It is about 39.37 inches.

Decimal parts of the principal metric units are expressed

by Latin prefixes; multiples are expressed by Greek prefixes.

The following is the table of linear measure. In this and the following tables the names of the units commonly used are in black type.

10 kilometers = 1 myriameter (Mm.).

Lengths that are expressed in English units in inches, feet, and yards, and miles, are expressed in metric units in centimeters and millimeters, meters, and kilometers, respectively.

NOTE. The metric system cannot be taught successfully without having the metric units in the hands of the pupils. The pupils should do some measuring with these units. There should be in the schoolroom a meter stick, a liter measure, a decimeter cube, a number of centimeter cubes, balances, and a set of metric weights.

Exercise 27

1. Give the meaning of centi, milli, kilo, deci, hekto, deka, myria.

2. Give the prefix that means .001, 1000, .1, .01, 10,000, 100, 10.

3. A meter equals how many centimeters? How many decimeters? How many millimeters?

4. A kilometer equals how many meters?

5. What metric unit would be used in stating the length of a lead pencil? In stating the distance from New York to Chicago? The length of your schoolroom? The thickness of a telephone wire?

6. How far apart are the longest divisions on a meter stick? The next longest? The shortest?

7. How many decimeters in 45 m.? How many centimeters? How many millimeters?

8. Reduce 3657 mm. to meters; to centimeters; to decimeters.

9. What change in the position of the decimal point must be made in reducing centimeters to meters? Meters to kilometers? Meters to millimeters?

10. Reduce 2.75 cm. to meters.

11. Reduce .0028 m. to millimeters.

12. Reduce 486.7 meters to kilometers.

13. Reduce 31 m. to centimeters.

14. Reduce .117 Km. to meters.

15. Reduce 5.66 dm. to meters.

16. A kilometer is how many inches? Show that a kilometer is approximately of a mile, and that a centimeter is approximately of an inch. Use these equivalents in the next six exercises.

17. A mile is approximately how many kilometers? 18. An inch is approximately how many centimeters? 19. A 75 mm. gun is how many inches in diameter? 20. A trench is 120 Km. long. It is how many miles long? 21. A book is 8.5 cm. thick. Express the thickness in inches.