19. Suppose a curious old miser to have laid up several bags of dollars containing the following sums, viz. 1 dollar, 10 dollars, 100 dollars, and 10000 dollars. 20. Then 1 bag of 1 dollar would represent I unit; I bag of 10 dollars, 1 ten; 1 bag of 100 dollars, 1 hundred; 1 bag of 1000 dollars, 1-thousand; and 1 bag of 10000 dollars, 1 ten thousand. 21. As the second bag and all the succeeding ones are each but a single collection, or but one thing, it may properly be called a unit, as well as the bag that contains but 1 dollar. 22. Hence, a series,' or a progressive2 order3 of units may be established in which each succeeding one shall be ten times the value of a former one. 23. Simple units may then be denominated the first order, tens, the second order; hundreds, the third order, and so on. 24. Thus in 4689, the 9 is 9 units of the first order; the 8, 8 units of the second order; the 6, 6 units of the third order; the 4, 4 units of the fourth order. 25. We see also that the value of figures depends on the places they occupy. 26. When 2 and 5, for instance, stand separately, they mean simply 2 units and 5 units; but placed together, they may mean either 25 units or 52 units. 27. The value of a figure standing alone, is called its simple value; when combined with other figures, its local value. 28. To express two thousand three hundred and forty-five, we write them as follows, viz. THOUSANDS HUNDREDS TENS UNITS Write the 2 in the Thousands' place; the 3 in the Hundreds' place; the 4 in the Tens' place; and the 5 in the Units' place. This is called Notation. 29. To ascertain if we have correctly written the number, begin on the right and say; units, tens, hundreds, thousands; then begin on the left and read, Q. Repeat the Table in which 10 units make 1 ten, &c.? 18. How many units are there in 2 tens? in 5 tens? tens in 50 units? in 100 units? in 89 units? [8 tens and 9 units.] tens in 95 units? in 105 units? [10 and 5 units.] tens in 165 units? hundreds, tens and units in 165 units? [1 hun. 6 tens and 8 units.] in 456 units? units in 4 hundreds 5 tens and 6 units? What is meant by a series of units? 22. Give an example? 20, 21. What constitute the several orders? 23. In 4689, for instance, point out the different orders? 24. On what does the value of a figure depend? 25. In expressing 2345, by figures, what places would each figure occupy? 28. How is it ascertained if it be correctly written? 29. What number will 1, 2, and 3 represent, taken together in the same order as they stand? A. One hundred and twenty-three. What number will 2, 3, 4, and 5 represent, taken in like manner? 1 SERIES, [L. series.] A regular succession of things; course; order 4 SUCCEEDING. Following in order; following in the place of another. giving to each figure the name of the place against which it stands ; thus 2 thousand 3 hundred and 45; which we find corresponds with the given number. This is called Numeration. 30. Write in words on the slate, the following numbers : 31. It is customary to separate large numbers by a comma, into parts or portions called periods of three figures each, beginning on the right. 32. The first period; as it contains units, tens of units, hundreds of units, is called the period of Units. 33. The next left hand period, for a similar reason, is called the period of Thousands, and so on as in the following. aree billion, four hundred fifty-six million, seven hundred eighty ine thousand, nine hundred and ninety-nine. Q. What are periods of figures? 31. What are the first, second, third, &c.. periods called? 32. 33. Repeat the Numeration Table II; as, units, tens, hun dreds, &c., as far as hundred billions? 34. What figures in the Table represent ninety? Nine hundred? Nine thousand? Eighty thousand? Seven Erared thousand? Six million? Fifty million? Four hundred million? Three cr Twenty billion? One hundred billion? 35. Write in words on the slate the following numbers. 4 8 read 8 billion, 8 53. 7 0 070 0 7 0,070 read 70 billion, 70 million, &c. 54.8 0 0 800.800 8 0 0 read 800 bill'n, 800 mill'n, &c. 55. 6,00 0,6 0 0,0 0 0 read 6 bill'n, and 600 thousand. 56.9 0 0 000 000 0 0 9 read 900 billion and 9. 57. By canceling1 all the ciphers in the last example the 900 billion and 9 becomes only 99. 58. Hence be careful to fill all vacant plans with ciphers.* RECAPITULATION. 59. NOTATION is the writing of numbers in figures; NUMERATION, the reading of them expressed in figures. RULE FOR WRITING NUMBERS. 60. Begin on the left and write each figure according to its value in the Numeration Table, taking care to supply all vacant places with ciphers. Q. What caution is given in respect to vacant places? 58. Give an example of its importance? 57. What is Notation? 59. Numeration? 59. What is the rule for writing numbers? 60. * The practice of reckoning only three figures to a period, is derived from the French. The English reckon six figures for a period, which would carry the millions' place in the above Table, into the billions' place. One billion then, by the French mode, expresses a number one thousand times sinaller than by the English method; which, as you may perceive, greatly diminishes the power of figures. But as the former is most convenient, it generally has the preference. 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 Read 333 thousand 333 quadrillion, 333 thousand 333 trillion, 333 thousand 333 bilan 333 thousand 333 million, 333 thousand 333. 1 CANCELING, [F. canceller.] Crossing; obliterating, annulling. PROOF, OR RULE FOR READING NUMBERS. 61. Begin on the right and numerate by saying units, tens, hundreds, &c.; then begin on the left and read, joining the name of its vlace to each figure; which, if it correspond with the given number, is correctly written. NUMERATION TABLE III. Hundred Octillions. Hundred Quintillions. 14 Hundred Quadrillions. Ten Billions. Millions. Hundred Hundred Thousands. UNITS. 5 5 5,5 5 5,5 5 5,5 5 5,5 5 5,5 5 5 5 5 5 5 5 5,5 5 5,555 62. Read 555 octillion, 555 septillion, 555 sextillion, 555 quintillion. 555 quadrillion, 555 trillion, 555 billion, 555 million, 555 thousand, 555. 63. Write in figures on the slate, the following numbers 64. Ninety-seven. 65. Four hundred and twenty-five. 66. Three thousand and five. 67. Forty-nine thousand five hundred and twenty. 68. Six hundred and fifty-two thousand five hundred. 69. Eight million nine hundred and forty thousand. 70. One hundred and one. 71. Five thousand and five. 72. Four thousand two hundred and eight. Q. What for reading numbers? 61. Repeat the Numeration Table III. How are thirty 5s in succession read? How would thirty 3s'be read? 1 PRIMITIVE. Original, not derived from any thing; primary. 2 PREFIXING, Uniting at the beginning; placing before. 3 NUMERALS. Of or belonging to number; consisting of numbers. 4 TERMINATION. Limiting; bounding; ending; end of a word. 5 MODIFICATIONS. Changing the forms; altering the appearance. 6 EUPHONY, [G. eu, good, and phone, sound.] An agreeable sound. 7 PREFIX. À letter, syllable, or word, put at the beginning of a word. 8 ONE, TWO, THREE, and up to TWELVE, are reckoned primitive (1) words. 9 THIRTEEN, FOURTEEN; THEE and TEN, FOUR and TEN, &c. 10 TWENTY, THIRTY, &c. are derived from TWO TENS, THREE TENS, &0 11 THE HUNDRED is from the Latin hun or hundred. 12 THE THOUSAND is derived from the Saxon thousand. This and the two preceding umerals (3) are usually considered as primitive in our language 13 THE MILLION is derived from the French million. 14 THE BILLION, TRILLION, QUADRILLION, &c. are formed by prefixing (2) the Latin numerals to the termination (4) illion, with such slight modifications (5) as euphony (6) requires. The Latin prefixes (7) are bis, twice; tres, three; quartuor, for; quinque, five; sex, six; septem, seven; octo, eight; novem, nine; decem, ten; undecim, eleven; duodecim, twelve; tredecim, thirteen, &c. These prefixes, with illion, make_Billion, Trillion, Quadrillion, Quintillion, Sextillion. Septillion, Octillion, Nonillion, Undecillion, Duodecillion, Tredecillion 73. Three hundred thousand five hundred. 74. Six million one hundred thousand. 75. Four million four thousand and forty-nine. 76. Seventeen million one hundred and twenty-five. 77. One billion, one million, one thousand and one. 78. Five hundred and twenty-one billion, three hundred million, three hundred thousand and one. 79. Five trillion, five billion, five million, five thousand and five hundred and fifty-five. 80. Six quadrillion, six hundred million, four hundred and fiftynine thousand and sixteen. 81. Two hundred and fifty quintillion, six quadrillion, two billion, three hundred and forty thousand.† Figures on the slate are written thus,— 1 2 3 4 5 6 7 8 9 0 SIMPLE ADDITION.' XI. 1. Add together 9 dollars, 7 dollars, 5 dollars, 8 dollars, 6 dollars, 4 dollars, and 3 dollars, thus ; XI. Q. How much is 33 and 9? What is the 42 called? See 7. + Remarks to the Learner. As very high numbers are somewhat difficult to apprehend; it may not be amiss to illustrate, by a few examples the value of the words million, billion, trillion, and quadrillion, according to the English notation. Suppose that a person employed in telling money, reckons a hundred pieces in a minute, and continues to do so twelve hours each day, he will take nearly fourteen days to reckon a million. A thousand men would take more than 38 years to reckon a billion. The inhabitants of the United States in 1820, were about 10 million. Now if we suppose all these persons had been constantly employed in counting money since the birth of Christ, they could not as yet have reckoned a trillion. Though we admit the earth, from the creation, to have been as populous as it is at present (being about 800 million,) and the whole human race to have been counting money without intermission; they could scarcely, as yet, have reckoned the five hun dredth part of a quadrillion of pieces. 1 ADDITION, [L. additio.] Any thing added; adding; joining; uniting two or more numbers in one sum. * (1). A. 42 dollars. (2). A. 42 tons. (3.) A 45 cents. (4.) A 52 ounces. (5.) A 46 mills. (6.) A. 54 hats. |