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the same value, each being equal to 4 or ; but when ciphers are placed on the left hand of a decimal, they decrease the value in a tenfold proportion. Thus, .4 is 4, or four tenths ; but .04 is 70, or four hundredths ; and .004 is too, or four thousandths. The figure next the separatrix is reckoned so many tenths; the next at the right, so many hundredths ; the third is so many thousandths; and so on, as may be seen by the following

TABLE. .

o Hundreds of Thousands.
er Tens of Thousands.
1 Millions.
A Thousands.

Hundreds.
o Hundred Thousandths.

Thousandths.

Tens.
er Ten Thousandths.
co Hundredths.

Tenths.
- Units.

Millionths.
A

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From this table it is evident, that in decimals, as well as in whole numbers, each figure takes its value by its distance from the place of units.

Note. — If there be one figure in the decimal, it is so many tenths; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c.

NUMERATION OF DECIMAL FRACTIONS.

Let the pupil write the following numbers. 1. Three hundred twenty-five, and seven tenths. 2. Four hundred sixty-five, and fourteen hundredths. 3. Ninety-three, and seven hundredths. 4. Twenty-four, and nine millionths. 5. Two hundred twenty-one, and nine hundred thousandths. 6. Forty-nine thousand, and forty-nine thousandths.

7. Seventy-nine million two thousand, and one hundred five thousandths.

8. Sixty-nine thousand fifteen, and fifteen hundred thousandths.

9. Eighty thousand, and eighty-three ten thousandths.

10. Nine billion nineteen thousand nineteen, and nineteen hundredths.

11. Twenty-seven, and nine hundred twenty-seven thousandths.

12. Forty-nine trillion, and one trillionth.
13. Twenty-one, and one ten thousandth.
14. Eighty-seven thousand, and eighty-seven millionths.

15. Ninety-nine thousand ninety-nine, and nine thousand nine billionths.

16. Seventeen, and one hundred seventeen ten thousandths. 17. Thirty-three, and thirty-three hundredths. 18. Forty-seven thousand, and twenty-nine ten millionths. 19. Fifteen, and four thousand seven hundred thousandths. 20. Eleven thousand, and eleven hundredths. 21. Seventeen, and eighty-one quatrillionths. 22. Nine, and fifty-seven trillionths.

23. Sixty-nine thousand, and three hundred forty-nine thousandths.

Let the following numbers be written in words.
27.86 86.0007 1.000007 16.300000007

5.6001 5.101016 , 1.315
15.716 34.1063 6.716678

0.0000001
161.3
15.0016 1.631

10.10101
87.006 16.1004 3.760701 1.000327

48.07

Section XXIII.

ADDITION OF DECIMALS. 1. Add 23.61 and 161.5 and 2.6789 and 61.111 and 27.0076 and 116.71 and 6151.7671 together.

OPERATION.
23.61

In this question, it will be perceived 161.5

that tenths are written under tenths, 2.6789 hundredths under hundredths, &c.; and 61.111 that the operation of addition is per

27.0076 formed as in addition of whole num-
116.71

bers.
6151.7671
6544.3846

Rule. -- Write the numbers under each other according to their value, add as in whole numbers, and point off from the right hand as many places for decimals as there are in that number which contains the greatest number of decimals.

2. Add together the following numbers : 81.61356, 6716.31, 413.1678956, 35.14671, 3.1671, 314.6. Ans. 7564.0052656.

3. What is the sum of the following numbers : 1121.6116, 61.87, 46.67, 165.13, 676.167895 ? Ans. 2071.449495. 4. Add 7.61, 637.1, 6516.14, 67.1234, 6.1234, together.

Ans. 7234.0968. 5. Add 21.611, 6888.32, 3.6167, together.

Ans. 6913.5477. 6. Add seventy-three and twenty-nine hundredths, eightyseven and forty-seven thousandths, three thousand and five and one hundred six ten thousandths, twenty-eight and three hundredths, twenty-nine thousand and five thousandths, together.

Ans. 32193.3826. 7. Add two hundred nine thousand and forty-six millionths, ninety-eight thousand two hundred seven and fifteen ten thousandths, fifteen and eight hundredths, and forty-nine ten thousandths, together.

Ans. 307222.086446. 8. What is the sum of twenty-three million ten, one thousand and five hundred thousandths, twenty-seven and nineteen millionths, seven and five tenths ? Ans. 23001044.500069.

9. Add the following numbers : fifty-nine and fifty-nine thousandths, twenty-five thousand and twenty-five ten thousandths, five and five millionths, two hundred five and five hundredths.

Ans. 25269.111505. 10. What is the sum of the following numbers : twenty-five and seven millionths, one hundred forty-five and six hundred forty-three thousandths, one hundred seventy-five and eightynine hundredths, seventeen and three hundred forty-eight hundred thousandths ?

Ans. 363.536487.

SECTION XXIV.

SUBTRACTION OF DECIMALS.

RULE. — Let the numbers be so written, that the separatrir of the subtrahend be directly under that of the minuend, subtract as in whole

numbers, and point off as many places for decimals as there are in that number which contains the greatest number of decimals.

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5. From 41.7 take 21.9767.

Ans. 19.7233. 6. From 29.167 take 19.66711.

Ans. 9.49989. 7. From 91.61 take 2.6671.

Ans, 88.9429. 8. From 96.71 take 96.709.

Ans. .001. 9. Take twenty-seven and twenty-eight thousandths from ninety-seven and seven tenths.

Ans. 70.672. 10. Take one hundred fifteen and seven hundredths from three hundred fifteen and twenty-seven ten thousandths.

Ans. 199.9327. 11. From twenty-nine million four thousand and five take twenty-nine thousand and three hundred forty-nine thousand two hundred, and twenty-four hundred thousandths.

Ans. 28625804.99976. 12. From one million take one millionth.

Ans. 999999.999999.

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11. Multiply 76.81 by 3.2. 12. Multiply .1234 by .0046. OPERATION.

OPERATION. 76.81

.1234 3.2

.0046 15362

7404 23043

4936 245.792

.00056764

RULE. — Multiply as in whole numbers, and point off as many figures for decimals in the product as there are decimals in the multiplicand and multiplier ; but, if there should not be so many figures in the product as there are decimals in the multiplicand and multiplier, supply the defect by prefixing ciphers. See Example 12th. 13. Multiply 61.76 by .0071.

Ans. .438496. 14. Multiply .0716 by 1.326.

Ans. .0949416. 15. Multiply .61001 by .061.

Ans. .03721061. 16. Multiply 71.61 by 365.

Ans. 26137.65. 17. Multiply .1234 by 1234.

Ans. 152.2756. 18. Multiply 6.711 by 6543.

Ans. 439 10.073. 19. Multiply .0009 by .0009.

Ans. .00000081. 20. Multiply forty-nine thousand by forty-nine thousandths.

Ans. 2401. 21. What is the product of one thousand and twenty-five, multiplied by three hundred and twenty-seven ten thousandths ?

Ans. 33.5175. 22. What is the product of seventy-eight million two hundred five thousand and two, multiplied by fifty-three hundredths ?

Ans. 41448651.06. 23. Multiply one hundred and fifty-three thousandths by one hundred twenty-nine millionths.

Ans. .000019737. 24. What is the product of fifteen thousand, multiplied by fifteen thousandths ?

Ans. 225. 25. What will 26.7 yards of cloth cost, at $5.75 a yard ?

Ans. $153.52,5. 26. What will 14.75 bushels of wheat cost, at $1.25 a bushel?

Ans. $18.43,75. 27. What will 375.6 pounds of sugar cost, at $0.125 per pound?

Ans. $ 46.95. 28. What will 26.58 cords of wood cost, at $5.625 a cord ?

Ans. $149.51,2.. 29. What will 28.75 tons of potash cost, at $125.78 per ton?

Ans. $3616.17,5.

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