APPLICATION OF DECIMALS.

102. The application of the principles of decimals and common fractions gives rise to several abbreviations in multiplication, division, and business transactions, of which the following are the most important:

CASE I.

103. To multiply by an aliquot part of 100.

An Aliquot Part of a number is the whole or mixed number which will exactly divide that number. Thus, 50, 331, 25, 20, 163, 121, etc. are aliquot parts of 100.

1. To multiply by 25.

This is equivalent to multiplying by 10o; hence the

RULE.

Annex two ciphers, or move the decimal point two places to the right, and divide by 4.

This is equivalent to multiplying by 100; hence the

RULE.

Annex two ciphers, or move the decimal point two places to the right, and divide by 8.

3. To multiply by 331.

This is equivalent to multiplying by 100; hence the

RULE.

Annex two ciphers, or move the decimal point two places to the right, and divide by 3.

Similar rules may be made for other aliquot parts of 100.

CASE II.

104. To divide by an aliquot part of 100.

This is equivalent to multiplying by 186; hence the

RULE.

Multiply by 8 and divide by 100.

This is equivalent to multiplying by 18; hence the

Similar rules may be made for other aliquot parts of 100.

PROBLEMS.

1. What will 72 yards of muslin cost at 12 cents a yard? 2. What will 32 yards of calico cost at 64 cents a yard? 3. What will 150 pounds of coffee cost at 33 cents a pound?

4. What will 48 pounds of butter cost at 33 cents a pound, and 64 dozen of eggs at 25 cents a dozen?

5. What is the cost of 24 yards of cloth at $1.16%, and 75 yards of muslin at 12 cents a yard?

6. What will 216 tons of ore cost at $163 a ton?

7. What will 429 tons of rails cost at $331 a ton?

8. What will 840 bushels of oats cost at 25 cents a bushel? 9. What will 215 pounds of beef cost at 20 cents a pound?

10. What will 126 pounds of sugar cost at 61 cents a pound?

11. What will 23 dozen of eggs cost at 25 cents a dozen? 12. What will 90 quarts of berries cost at 12 cents a quart?

CASE III.

105. To find the cost when the quantity and the price of 100 or 1000 are given.

1. What will 1225 bricks cost at $9 per 1000?

PROCESS.
$9
1.225

If 1000 bricks cost $9, 1225 bricks, which is 1.225 times 1000, will cost 1.225 times $9, or $11.025.

$11.025, Ans.

RULE.

Multiply the price by the quantity, and point off two places for the price per hundred or three places for the price per thousand. What is the cost

2. Of 5200 shingles at $4.75 per thousand?
3. Of 6875 cigars at $6.50 per thousand?
4. Of 3480 feet of boards at $34 per thousand?
5. Of 5760 bricks at $9.25 per thousand?
6. Of 10824 railroad ties at $15 per hundred?
7. Of 5820 chestnut rails at $4 per hundred?
8. Of 625 pounds of beef at $11.25 per hundred?
9. Of 1425 pounds of freight at $.45 per hundred?
10. Of 276 pounds of pork at $9.50 per hundred?
11. Of 8560 pounds of coal at $6.50 per ton?
SUGGESTION. Take half the price per ton, and proceed as before.

12. Of 6780 pounds of hay at $15.50 per ton?
13. Of 16825 pounds of bone-dust at $20.50 per ton?
14. Of 6220 pounds of wool at $540 per ton?
15. Of 4280 pounds of oats at $22.50 per ton?
16. Of 8040 pounds of cast iron at $120 per ton?

MISCELLANEOUS EXAMPLES.

106.-1. Reduce .0643 to a common fraction.

2. Reduce to a decimal.

3. Add .0162 and 209

2500.

4. Subtract .00865 from 1.02.
5. Multiply 54368 by .0025.
6. Multiply 621.78 by 331.
7. Divide 18.1771 by 6.7.

8. Divide 86.215 by 12.

9. Reduce 1.00163 to a mixed number. 10. Add 18.94 +2.041 +4.36%.

11. Subtract .067951 from 2.00701.
12. Multiply 1.675432 by 10000.
13. Divide 817.1456 by .000001.
14. Multiply 54.063 by 1.11.
15. Divide 102.056 by 331.
16. Reduce 12455 to a decimal.
17. Multiply 682.154 by .0001.
18. Divide 250000 by .00005.
19. Divide .000025 by 50000.
20. Multiply 81.4563 by 3331.
21. Subtract .0406008 from .07.
22. Reduce .143 to a common fraction.
23. Reduce .0011 to a common fraction.

11

24. Add 2.84 + + 14.01 + 100.001.

64

25. Multiply 42.37, .0002, 400, and.

53

26. Reduce to a decimal.

27. Add 1.13 +2.2216 +3.333 + 4.4444. 28. Subtract 11.11 from 22.23.

29. Subtract 33.3 from 33.333 + 3.3.

30. Multiply the sum of 1000 + .001 by .001.

31. Divide the difference between .1 and .001 by .1.

32. Divide the sum of .5 and .5 by their product; also the product of .5 and .5 by their sum.