A Complete Arithmetic

2. Write 18 decameters, 4 meters, 6 decimeters, and 7 centimeters in terms of decameters. In terms of meters. In terms of decimeters. In terms of centimeters.

3. Write 16 hectometers, 6 decameters, and 5 centimeters in terms of meters. In terms of decameters. In terms of decimeters.

4. Write 8 D., 5, 4 cl., 3 ml. in terms of liters. In terms of decaliters. In terms of milliliters.

5. Write 6 Kg., 4 Dg., 68., 7 cg., and 5 g. in terms of grams. In terms of decigrams. In terms of decagrams.

6. Write 64 sq. Dm., 45 sq. m., and 18 sq. cm. in terms of square meters. In terms of square decimeters.

7. Write 8 cu. Dm., 7 cu. m., and 6 cu. dm. in terms of cubic meters. In terms of cubic decameters.

8. Write 14 cu. Dm., 137 cu.m., and 375 cu. cm. in terms of cubic meters. In terms of cubic decimeters.

REDUCTION OF METRIC NUMBERS.

316. The reduction of metric numbers may be effected by the following principles:

Prin. 1.—A metric number may be reduced to a lower denomination by moving the decimal point one place to the right for each decrease in the denomination.

Thus, 64.416

644.161.

64416 cl, etc.

Prin. 2.-A metric number may be reduced to a higher denomination by moving the decimal point one place to the left for each increase in the denomination.

634.5 dm.

D1.

cm.

6441.6 al.

Thus, 6345

These principles do not apply to the tables of square and cubic measure. In these tables the decimal point must be moved

63.45

Dm.

6.345 etc.

two places for each change in the denomination of square meas ure, and three places for each change in the denomination of cubic measure.

Thus, 45.6747 8q. Dm.

Reduce

4567.47 sq.m.

148 cu. mm. = .148 ca. cm. = .000148 cu. dm., etc.

456747 sq. dm.

WRITTEN EXERCISES.

1. 7.321 mg to centigrams.

2. 4567 Dg to decigrams.

3. 86754 cm. to kilometers.
4. 47654 mm. to decameters.
5. 47375cl to hectoliters.
6. 6.4765 Kl. to centiliters.
7. 6756 cm. to meters.
8. 6.476 to liters.

HI.

9. 93456 to kilograms.

10. .478654 Mg to centigrams.
11. 8476543 sq.m. to square kilometers.
12. 4.786953 cu.m. to cubic centimeters.

13. 95432 cu. mm. to cubic decimeters.

14. .00579 Kl. to liters.

15. 48.567 Mg. to metric tons.

etc.;

16. What is the weight in decagrams of a liter of distilled water at 39.2° Fah.?

17. What is the weight in kilograms of a stere of distilled water?

18. Reduce 45.16 cu. cm. to centiliters.

19. Reduce 42.87 Ha. to ares.

20. What is the weight of 16.51 cu. m. of water in myriagrams?

21. How many centiliters of water will weigh 184 mg. ? 22. How many decaliters of water will weigh 16.84 Kg.?

ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION OF METRIC NUMBERS.

317. If metric numbers be reduced to decimals of the same denomination, they may be added, subtracted, multiplied, and divided as ordinary denominate decimals.

WRITTEN EXERCISES.

1. Add 46 dm., 2.737 Dm., and 1.82453 Hm.

Reducing to the decimal of a meter and adding, we have

46 dm. 2.737 Dm. 1.82453 Hm.

2. Subtract 277.94 dg. from 14.5786 Dg.

Reducing to the decimal of a gram and subtracting, we have

14.5786 Dg.
277.94 dg.

625

4.6 m.

27.37
182.453

214.423 m.,
m. Ans.

145.7868.

27.794

117.992, Ans.

3. Multiply 432.15 d. by 4, and express the result in decaliters.

Reducing to the decimal of a liter and multiplying, we have

43.215 1.

172.86017.286 D1., Ans.

4. Divide 1562.5 cm. by 1.25, and express the result in meters. Reducing to the decimal of a meter and dividing, we have 1.25)1562.5 cm. (1250 cm. 12.5 m., Ans. 125

cm.

312

250

5. Divide 320.84 dg. by .26 Dg.

Reducing to the decimal part of a gram and dividing, we have

2.6 8.)32.084 (12.38, Ans.

meters.

Add

6. 432.14 m., 10.2325 Dm., 62.8 m., and 7512 cm.

7. 8214, 3278 H., .6213 K., and 4156 ml.

8. 46.352 g., 12.34 dg., 40400 cg., and 213 mg.

9. 2.48213 sq. Dm., 12467.8 sq. dm., and 356.789 sq.m. 10. .621543 cu. Dm, 321.767 cu. m., and 143254 cu. dm.

Subtract

11. 456.7 d. from 11.6214 HI. 12. .12371 Km. from 48564 cm.

104

15. 10830.2 sq. dm. from 8.64321 sq. Dm.

Multiply

16. 4.62 d. by 1.23, and express the result in decaliters. 17. 4.3216 m. by 2.4, and express the result in decimeters. 18. 3216 by 23.6, and express the result in kiloliters. 19. 1.3578 sq. Dm. by 6.3, and express the result in limeters.

cl.

square mil

20. .432 cu. Dm.

13. 97004 mg. from 1.25782 g. 14. 678 cu. dm. from .432

cu. Dm.

by .71, and express the result in cubic centi

dm.

23. .9672 by 26
24. 8.11332 by 372

Km.

mm.

cg.

25. 1788.57 8 by 6.3, and express the result in kilograms. 26. 1.05156 Dm. by .56, and express the result in centimeters.

318. To reduce a metric number to a common denominate number, or a common denominate number to a metric number.

4.228 Dm.

1. Reduce 4.228 Dm. to feet.

PROCESS.

2. Reduce 4 rd. and 6 ft. to meters.

PROCESS.

42.28 m.

.3048 m.
72

Reduce

72 ft.

6096 21336 21.9456 m.

WRITTEN EXERCISES.

are equal to 42.28 m.

4.228 Dm. In 1 meter there are 3.28 ft., and in 42.28 m. there are 42.28 times 3.28 ft., or 138.6784 feet.

4 rd. and 6 ft. equal 72 ft. In 1 foot there are .3048 m., and in 72 feet there are 72 times .3048 m., or 21.9456 m.

Measures of Length.

3. 8.05 Dm. to feet.
4. 2.046 Km. to yards.
5. 80 Km. to miles.

9. 600 to acres.

Measures of Surface.

6. 320 yards to decameters. 7. 5 miles to hectometers. 8. 2000 feet to kilometers.

10. 4.21 a to square yards. 11. .635 sq. Mm. to sq. rods.

12. 1260 sq. yd. to sq. Dm.
13. 2 A. and 25 P. to ares.
14. 640 sq. mi. to sq. kilometers.

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A Complete Arithmetic: With Oral and Written Exercises