6. In 3687 metres how many dekameters? how many hectometers? how many kilometers?

7. In 85 kilometers how many meters? how many hectometers? how many dekameters?

8. Express in meters the following, and add them: 1000 millimeters, 5 dekameters, 100 decimeters, 929 centimeters. Ans. 70.29m 9. Express in meters the following numbers, and add them: 4075 centimeters, 27 dekameters, .075 kilometers.

Ans. 385.75m. 10. Express in kilometers the following, and add them: 2400 meters, 500 dekameters, .79 myriameters. Ans. 15.3km

11. Express in kilometers the following, and add them: 1000000 meters, 84 hectometers, 2005 myriameters, 870000 decimeters. Ans. 21145.4km

12. If a man in a journey travelled 12 kilometers, 4 hectometers in one hour, 20.7 kilometers in the next hour, and 29 kilometers in the third, how many kilometers did he travel in the three hours? Ans. 62.1km. 13. From A to B is 247 kilometers; if C is 50.8 kilometers beyond B, all being in the same straight line, how many kilometers is it from A to C. Ans. 297.8km.

14. If 7.08 kilometers are taken from 42 kilometers, how many meters will remain? Ans. 34,920m. 15. The distance round a certain park is 2.58 kilometers; how many meters will a man go who rides around it six times? Ans. 15,480m.

16. A schoolboy walked one third around the above park in 12 minutes; how many meters did he walk in 1 minute?

Ans. 71.66m+.

17. The latitude of Chicago is 42° N.; how many kilometers

is it from Chicago to the equator?

18. How many kilometers is it from Pole?

Ans. 4666.66m+. Chicago to the North

Ans. 5333.33km+.

19. How many meters are there in 1' of latitude?

Ans. 1851.8m+.

MEASURES OF SURFACE.

8. In the measurement of small surfaces the Square Meter is the primary unit.

Each side of a square meter is 10 decimeters in length, and hence a square meter contains 10 X 10 = 100 square decimeters.* Each side of a square decimeter is 10 centimeters in length, and hence a square decimeter contains 10 X 10 = 100 square centimeters, etc. Thus it may be seen that while measures of length increase and decrease by a scale of tens, measures of surface increase and decrease by a scale of hundreds.

1. How many sq. decimeters equal 1 sq. meter? 2 sq. meters? 2. How many sq. centimeters equal 1 sq. decimeter? 1 sq. meter?

3. How many sq. millimeters equal 1 sq. centimeter? 1 sq. decimeter? 1 sq. meter?

9. The manner of writing the different orders of units of surface is illustrated by the following

*The teacher may readily show this by making upon the blackboard a diagram one meter square, dividing each side into ten equal parts, and drawing lines through the points of division parallel to the sides. By this process he will have a square meter divided into one hundred smaller squares, each of which is one decimeter long and one decimeter wide, and hence is a square decimeter. In the same way a square decimeter may be shown to equal one hundred square centimeters. By this means the pupil will have a clearer idea of the size of these measures than by any diagram which could be presented in this book.

Since the values of units of surface increase and decrease by a scale of hundreds, it is necessary, in writing numbers denoting surfaces, to allow two places for decimeters, two for centimeters, and two for millimeters: thus,

4 sq. meters, 8 sq. decimeters, are written 4.08sqm.

If the decimal part of an expression contains an odd number of figures, a zero may be annexed to it before reading it in terms of the lower orders; thus, 1.1sqm may be written 1.10sqm, and read 1 sq. meter, 10 sq. decimeters.

In what places at the right of the decimal point are sq. decimeters written? sq. centimeters? sq. millimeters?

10. EXAMPLES.

1. Express the following numbers in sq. meters and add them : 5 sq. decimeters, 87 sq. meters, 26 sq. centimeters, 5.9 sq. Ans. 92.9526sq m.

meters.

2. Express the following numbers in sq. meters and add them: 45 sq. decimeters, 118 sq. millimeters, 3 sq. centimeters, 347 sq. centimeters. Ans. .485118sqm.

3. How many sq. meters are there in a rectangular court 5 meters long and 22 meters wide? Ans. 110sq m

4. How many sq. decimeters are there in a rectangular pane of glass 3 decimeters long and 2 decimeters wide? Ans. 6sq decim 5. How many sq. centimeters are there in a rectangular plate of silver 8 centimeters long and 72 millimeters wide?

Ans. 57.6 cm 6. What is the cost of polishing the surface of a rectangular piece of marble 2 meters 8 decimeters long, and 1 meter 2 decimeters wide, at $2.50 per sq. meter? Ans. $8.40.

7. How many sq. meters in a square whose side is 5 meters, 23 centimeters long? Ans. 27.3529sqm.

8. What is the width of a rectangular picture, whose surface contains 2.124 sq. meters, and whose length is 1 meter, 8 decimeters? Ans. 1.18m.

11. We have seen that the meter and its subdivisions are used to measure small surfaces; but to measure surfaces of great extent, as a field, a township, etc., the Are is the primary unit.

The Are is a square whose side is 10 meters and whose surface contains 100 square meters.

In land measure, centares, ares, and hectares only are used. NOTE.-The are equals 119.6 square yards, nearly 4 square rods, or about of an acre. The hectare equals about 2 acres.

1. In 1 hectare how many ares? how many centares?
2. In 13 hectares how many ares? how many centares?
3. 1 centare is what part of an are? of a hectare?
4. What part of an are is 15 centares?

12. The following table shows the method of writing numbers in land measure, also the relation of the units to those given in the preceding table (Art. 9) as measures of surface.

1. Express the following in ares and add them: 1.3 hectares, 155.5 ares, 43 hectares, 26 centares.

Ans. 4585.76ar.

2. Mr. Jenks owned 25 hectares, 32 ares, 16 centares of land, and afterwards bought 36 hectares, 5 ares, 8 centares; how many ares did he then have? Ans. 6137.24ar.

3. A had 6 hectares, 7 ares, 9 centares of land, and sold of it at $54 an are; how many dollars did he receive for what he sold?

Ans. $5960.52.

MEASURES OF VOLUME.

14. In the measurement of solids, the Cubic Meter is the primary unit.

=

Each edge of a cubic meter is 10 decimeters in length, and hence a cubic meter contains 10 X 10 X 10, 1000, cubic decimeters.* Each edge of a cubic decimeter is 10 centimeters in length, and hence a cubic decimeter contains 10 X 10 X 10, =1000, cubic centimeters, etc.

Thus it may be seen that while measures of length increase and decrease by a scale of tens, measures of volume increase and decrease by a scale of thousands.

TABLE.

1000 cu. millimeters (cu mm) = 1 cu. centimeter (cu cm).

1000 cu. centimeters

1000 cu. decimeters

(cu decim).

1 cu. decimeter (cu decim = 1 CU. METER (cu m).

EXERCISES.

1. How many cu. decim. = 1 cu. m.?

2. How many cu. cm. = 1 cu. decim.? 1 cu. m.? 3. How many cu. mm. = = 1 cu. em.? 1 cu. decim.? 1 cu. m.? 4. What part of a cu. m. is 1 cu. decim.? 1 cu. cm.? 1 cu.mm.? 15. The manner of writing the different orders of units of volume is illustrated by the following

It may be seen by the table above, that in writing numbers denoting volume, three places must be allowed for cubic decimeters,

The pupil has already seen that a square meter contains 100 square decimeters. A cubic meter has a square meter for its base. If the solid resting upon this base were but 1 decimeter in height, it would contain 100 cubic decimeters, but since it is 10 decimeters in height, it must contain 10 times as many, or 1000 cubic decimeters.