31. Read the following, and notice the effect of moving the decimal point one, two, three, or more places to the right:

.4862; 4.862; 48.62; 486.2; 4862. 32. Read the following, and notice the effect of placing one, two, three, or more zeros between the decimal point and the first decimal figure:

26.4; 26.04; 26.004; 26.0004; 26.00004. 33. Read the following, and notice the effect of placing zeros on both sides of the decimal point:

3.3; 30.03; 300.003; 3000.0003. 34. Read the following, and notice the similarity of sound and difference of value:

404000; 400.004; 404; 303000; 300.003; .303.

NOTATION OF DECIMALS.

92. In writing a decimal, write the numerator as a whole number, and then place the decimal point so that the right-hand figure expresses the denomination required. Write in figures

1. Four tenths. Six tenths. Nine tenths. 2. Five hundredths. Forty-five hundredths. 3. Seven thousandths. Seventy-five thousandths. 4. Eighty-five hundredths. Eight, and five tenths. 5. Sixty, and six hundredths. 125 thousandths. 6. Three hundred and four ten-thousandths. 7. Five, and fifteen thousandths. One millionth. 8. Ninety, and nine hundredths. Four millionths. 9. One hundred and twenty, and four millionths. 10. Sixty-five hundred, and sixty-five hundredths. 11. Seventy-five thousand, and seventy-five thousandths.

12. Three hundred, and three thousandths.
13. Three hundred and three thousandths.
14. Eight tens. Eight units. Eight tenths.
15. Four hundred. Four tens. Four tenths.
16. Six thousand. Six thousandths.
17. Twenty-five tens. Twenty-five tenths.
18. Twenty-five hundred. Twenty-five hundredths.
19. 325 hundredths. 325 tenths.
20. 125 ten-thousandths. 125 millionths.
21. 4211 hundredths. 4211 thousandths.
22. 16, and 25 thousandths.
23. 9, and 9 ten-millionths.
24. 1007 millionths. 14 ten-millionths.
25. Four and one-half tenths.
26. Twenty-four and two-thirds hundredths.
27. One-half tenth. One-third hundredth.

35. 33%

100

30.

6 2 5

Write the following as decimals :
28. o
31. 861030 34. 163.

37. 125 126 29. 10 32. 625

38. 807660 TOT 1000 33. 4300 36. 21610600 | 39. 7006700

. Write the following as fractions : 40..5. 44...42835. 48. 2000.6.

52. .331. 41. .05. 45. 4.2835. 49. 200.06.

53. .667. 42. .005. 46. 42.835. 50. 20.006. 54. .163. 43. .0005. 47. 428.35. 51. 2.0006.

55. .371. 93. Principles.—1. Annexing ciphers to a decimal does not alter its value. Take as an example 3 = 16.

.3 becomes .30 oo by annexing one cipher.

.3 becomes .300 13:00% by annexing two ciphers, etc. Hence the value is not changed.

30 100

2. Prefixing ciphers to a decimal diminishes its value ten times for every cipher prefixed. Take as an example .3 = %.

.3 becomes .03 To by prefixing one cipher.

.3 becomes .003 Toto by prefixing two ciphers, etc. Hence the value is diminished ten times for each cipher prefixed.

3. Moving the decimal point to the right increases the value of the decimal ten times for every place passed over. Take as an example .333 =

.333 becomes 3.33 ist by moving the decimal point one place.

.333 becomes 33.3 3303 by moving it two places, etc. Hence the value is increased ten times for each place passed over.

4. Moving the decimal point to the left diminishes the value of the decimal ten times for every place passed over. Take as an example 33.3 =

33.3 becomes 3.33 ili by moving the decimal point one place.

33.3 becomes .333 18 by moving it two places, etc. Hence the value is diminished ten times for each place passed over.

3 3 3
1000

REDUCTION OF DECIMALS.

CASE I.

94. To reduce a decimal to a common fraction.

Express the decimal as a common fraction, and reduce it to its lowest terms.

Reduce the following decimals to common fractions : 2. .25.

5. .375. 8. 10.10. 11. 10.3750. 3. .85.

6. .625. 9. 4.3125. 12. 2.00125. 4. .64.

7. .875. 10. 12.9375. 13. 4.0125.

14. Reduce .16} to a common fraction. PROCESS.—.16;

163

, Ans. 100

15. .33 16. .663 17. .181 18. 4.351. 19. 5.058 20. 6.14. 21. 22.03. 22. 41.46.

23. 48.78 24. 25.833. 25. 81.463 26. 42.0911 27. 14.65. 28. .0005. 29. 1.245. 30. .0725.

31. .0225.
32. .6253
33. 4.373
34. 4.83
35. .034
36. 4.00z.
37. 17.00%
38. 8.66ş.

39. 12.04
40. 26.03.
41. 75.75.
42. 400.875.
43. 375.375.
44. 112.0625.
45. 2.0025.
46. 45.45.

CASE II.

95. To reduce a common fraction to a decimal.

WRITTEN EXERCISES.

1. Reduce š to a decimal. PROCESS.

equals of 3. 8)3.000 3 equals 30 tenths; } of 30 tenths is 3 tenths, and 6 .375, Ans. tenths remaining; 6 tenths equals 60 hundredths; f of

60 hundredths is 7 hundredths, and 4 hundredths remaining; 4 hundredths equals 40 thousandths; } of 40 thousandths is 5 thousandths. Hence equals .375.

RULE.

Annex ciphers to the numerator and divide by the denominator; point off as many decimal places as there are ciphers annexed.

111 2 56

16.

Reduce the following fractions to decimals :
1.

13. . 24. 183.
3. .
14. .

25. 9.25
15. 1.

26. 47.
5. ..

27. 5z.
6. .
.

28. 710
18. 1 29. 84
8. 1
19. 1.

30. 9.
9. a. 20. 11.

31. 7516 10. 3. 21. 5

32. 431 11. 16.

22. 9. 33. 1719

23. 7. | 34. 4231 257

17. 6

35. 105675 36. 37. 1664: 38. 4.00% 39. 1.329. 40. 6.0033 41. 2.0013 42. 4.0627. 43. 8.703. 44. 1.00.. 45. 40.001,

17

12. 13

19

ADDITION OF DECIMALS.

WRITTEN EXERCISES.

96.-1. Add 4.26, 12.005, and 126.4.
PROCESS.
4.26

We write the numbers so that their decimal points are 12.005

in the same vertical column, and add as in whole numbers, 126.4 142.665

placing the decimal point between units and tenths. Add

2. 28.32, 47.16, 35.08, 9.9, 12.001.'
3. 126.2, 26.37, 7.425, .6243, 250.1256.
4. .7802, 6.321, 89.42, 172.8, 4216.
5. 40.002, 7.08, 123.4567, 400.005.
6. .9374, 13.21, 45.135, 1.0006, 82.16.
7. 4.2, 16.73, 141.154, 7832.1654.

16.

12.
13.
14.

15. 8. 4.81 + 123.478 + 120.042 + 75.4 9. 63.45 + 2.3 + 74.6 + 62.04 10. 100.027 + 52.67 + 634.842 + 4.7 11. 53.2 + 40.732 + 3.5

+ 432.683