421. Examples for the Slate.

Change the following to meters:

Addition, Subtraction, Multiplication, and Division of Metric

Numbers.

422. ILLUSTRATIVE EXAMPLE. add 14.83 Dm, 75.6 Hm, and 948 cm.

WRITTEN WORK.

Dm

=

=

148.3 m 7560.

14.83 75.6 Hm

948 c

cm

=

9.48

7717.78 m

Change to meters and

Explanation. When these expressions have been changed to meters, they are all of the same denomination, and the sum is found in the same way as in the addition of simple numbers.

423. Numbers expressing metric measures and weights are added, subtracted, multiplied, and divided by the same rules as apply to simple numbers.

424. Examples for the Slate.

19. Add 5.6m, 24.07 m, 30.5m, and 7.508 m.

20. Express as meters and add 582 cm, 6428 dm, and 495 mm. 21. Express as meters and add 369 Dm, 4073 Hm, and 5 Km. 22. Add 48.06 m, 709.63m, 3708.9m, 800.9", and express the answer in kilometers.

23. If 7 Km be taken from 42 Km, how many meters remain? 24. From 87.04m take 42 cm.

25. The distance round a certain park is 2.58 kilometers. How many meters will a man go who rides around it six times? 26. A school-boy walked one third around the above park in 12 minutes. How many meters did he walk in 1 minute? 27. How many kilometers in 36.68 m × 2004 ?

28. Divide 38.07 m by 4 and by 3, and add the answers. 29. Ellen's hoop is 3.6m around. How many times will it turn in rolling a distance of 1.08 Km ?

MEASURES OF SURFACE.

425. The units used in measuring surfaces are squares, each having sides equal to a unit of long measure.

Thus, a square meter is a square having sides one meter long; a square decimeter is a square having sides one decimeter long; etc.

426. Exercises.

a. How many square decimeters in a square meter? Illustrate by drawing a square meter on the blackboard or on the floor and dividing it into square decimeters.

b. How many square centimeters in a square decimeter ? Illustrate by drawing a square decimeter on your slate and dividing it into square centimeters.

c. How many square meters in a square dekameter?

427. The square dekameter, when used as a unit of land measure, takes a special name, and is called an ar. One hundredth of an ar, which is one square meter, is called a centar. A hundred ars, equal to one square hektometer, is called a hektar.

428. Square Measure.

100 square millimeters (sq mm): = 1 square centimeter (sq cm). 100 square centimeters = 1 square decimeter (sq dm).

100 square decimeters 100 square meters

= 1 square meter (sq m)
= 1 square dekameter

= 1 centar (ca).

= 1 ar (a).

square hektometer

= 1 hektar (Ha).

100 square dekameters = 1

100 square hektometers = 1 square kilometer (sq Km).

429. As the units of square measure form a scale of hundreds, in writing numbers expressing surface two decimal places must be allowed for each denomination.

Thus, 45 sqm 4 sq dm 86 sq cm are written 45.0486 sqm; and 7 Ha 6a 5 ca are written 706.05 a.

430. Examples for the Slate.

30. How many square meters of carpeting will be required to carpet a room 5.3m long and 4.5m wide?

31. How many meters of carpeting 0.7m wide will be required to carpet a room 4m long and 3.5m wide?

32. What is the cost of polishing the surface of a rectangular piece of marble 2.8 meters long and 1.2 meters wide, at $2.50 per sq. meter?

33. In a piece of land 15 m long and 14.5m wide are how many square meters or centars? how many ars?

34. Express the following in ars and add them: 1.3 hektars, 155.5 ars, 43 hektars, 26 centars.

35. A had 6 hektars, 7 ars, 9 centars of land, and sold 0.2 of it at $54 an ar. How much did he receive for what he sold ?

MEASURES OF VOLUME.

431. The units used in measuring cubic contents, or volume, are cubes, each having its edges equal to a unit of long measure.

Thus, the cubic meter is a cube having edges one meter long; a cubic decimeter is a cube having its edges one decimeter long; etc.

432. Exercises.

a. How many cubic decimeters in a cubic meter?

b. How many cubic centimeters in a cubic decimeter? Illustrate by means of a cubical block having edges one decimeter long, marked off into centimeters.

433. The cubic meter, when used as a unit of measure for wood and stone, takes a special name, and is called a

ster.

434. The cubic decimeter, when used as a unit of liquid or dry measure, is called a liter.

435. Cubic Measure.

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

= 1 cubic decimeter (cu dm) = 1 liter,

1000 cubic centimeters

437. As the units of cubic measure form a scale of thousands, in writing numbers expressing volume three decimal places must be allowed for each denomination. Thus, 427 cum 29 are written 427.029003 cu

cu dm 3

cu cm

cu m

438. As the units of wood measure form a scale of tens, only one decimal place is needed for each denomination. Thus, 7 dekasters 5 sters 6 decisters are written 75.6 sters.

439. Examples for the Slate.

36. Express the following in cubic meters and add them: 7 cu. meters 40 cu. decimeters; 5 cu. meters 3 cu. decimeters 19 cu. centimeters; 25 cu. centimeters 49 cu. millimeters.

37. How many cubic meters of earth must be removed to dig a cellar 14.5m long, 4.6m wide, and 2.3m deep?

38. At $1.25 a cubic meter, what will it cost to dig a trench 75.5m long, 2.2m wide, and 1.8m deep?

39. How many loads of earth, each filling 2.25 cum, will fill a space 15.4m long, 12" wide, and 4.5m deep?

40. If a cubic centimeter of gold is worth $12.50, what is the value of a brick of gold 2.4 cm long, 1.3 cm wide, and 0.75 cm thick?

41. If I burn 27 sters of wood in the three winter months, what must be the length of a pile 1 meter wide and 3 meter high to last a month, and what will it cost at $2.25 a ster?

MEASURES OF CAPACITY.

440. The primary unit of measure for all substances that can be poured into a dish or box is the liter.

441. A liter is equal in volume to one cubic decimeter. 442. Larger and smaller measures are derived from the liter in the same way that longer and shorter measures are derived from the meter, that is, by taking decimal multiples and subdivisions.

NOTE. The milliliter is employed in computations, but rarely, if ever, in actual measurements. Chemists and druggists use cubic centimeters instead of milliliters.

444. Examples for the Slate.

42. If one hektoliter of kerosene costs $20, what is the price of a liter?

43. What must be paid for 2.5 liters of milk each day for a week, at 7 cents a liter?

44. From a vessel containing 1 hektoliter of syrup, 25 liters were drawn out. How many liters remained?

45. How many hektoliters of oats can be put into a bin that is 2m long, 1.3m wide, and 1.5m deep?

46. What must be the length of a bin 1 meter wide and 1 meter deep, to contain 4500 liters of grain?