8. The UNIT, which occupies the lowest place in the scale of whole numbers, means a single thing; that is, one; as, 1 hat, 1 boy. 9. The TEN, which means 10 units, is the least number that is formed by the union1 of two single characters, to wit: by annexing❜ the cipher to the figure 1, thus, 10; twenty, thus, 20; thirty, thus, 30, &c. 10. The HUNDRED, which is ten times 10 units, is formed by annexing two ciphers to the figure 1, thus, 100; two hundred, thus, 200; three hundred, thus, 300, &c. 11. The THOUSAND, which means ten times 100 units, is formed by annexing three ciphers to the figure 1, thus, 1000; two thousand, thus, 2000; three thousand, thus, 3000, &c. 12. The TEN THOUSAND, which is ten times 1000 units, is written thus, 10000; one hundred thousand, thus, 100000, &c. 13. In these examples, every additional3 cipher increases the value of the figure 1, ten times, by removing it one place further towards the left. 14. When a cipher or ciphers occur on the extreme left of other figures, they possess no value, as, 01; or 001, or 0001, each of which examples means simply 1. 15. In general, the removal of any figure one place further towards the left, enhances its value TEN TIMES. 16. Thus in 1111, the first figure on the right means 1 unit; the next, on the left 10 times 1 unit, or 10; the next, 10 times 10 units or 100; the next, 10 times 100 units, or 1000; all making one thousand one hundred and eleven. 17. Hence numbers increase from the right to the left in a TENFOLD proportion, as in the following Table. Q. What is meant by the unit? 8. How is the ten formed? 9. How, the hundred? 10. How, the thousand? 11. How, the ten thousand, and so on? 12. What effect has the cipher in these examples? 13. What does the figure 1 with either one, or two, or three ciphers prefixed represent? 14. What is the effect of removing a figure to the left? 15. What does each figure 1 in 1111 mean? 16 What is the law of increase? 17. 1 UNION, [L. unus, one.] Forming into one; bond; affection; concord. 5 EXTREME, [L. extremus, the last.] Outermost; fatherest; most pressing. 6 ENHANCES, Raises; lifts; advances; increases; heightens; aggravates. 7 TENFOLD. [ten and fold.] Ten times more in degree or extent. 8 PROPORTION, [L. proportio.] Equal degree or equal rate; symmetry 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 1 unit; 1 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 dellars, 1 ten thousand. 21. As the second bag and all the succeeding ones are each but a ingle collection, or but one thing, it may properly be called a unit, as well as the bag that contains but I dollar. 22. Hence, a series,' or a progressive order 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 denominated3 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 CO 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 num. ber 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? J SERIES. [L. series.] A regular succession of things; course; order 2 PROGRESSIVE. Going forward, advancing or increasing gradually. 3 ORDER, L. ordo. F. ordre.] Method; a mandate; rule, rank, class. 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. 0 00 000 000 000 000 00 000 000 700 000 80 000 9 900 90 read 100 billion read 3 billion. read 400 million. read 50 million. read 6 million. read 700 thousand. read 9 thousand. read 9 hundred. 123 4 5 6 7 8 9 999 read one hundred wenty three billion, four hundred fifty-six million, seven hundred eighty nine 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 ety? Nine hundred? Nine thousand? Eighty thousand? Seven hundred thousand? Six million? Fifty million? Four hundred million? Three billion? Twenty billion? One hundred billion? 35. Write in words on the slate the following numbers. 9 0,0 0 0 44. 7 8,6 4 31 45. 46. 42. 3,0 0 0,0 0 0 2,4 6 5,7 8 9 40 0 0,0 0 0 48. 7,3 6 2,49 1,7 23 5 0,00 0,00 0,00 0 49. 50. 43. 52. 2 3,45 6,8 9 2 8 0 0,0 0 0 000 000 51. 9 8 7,3 6 5,2 14,7 18 8 008 008 0 0 8 read 8 billion, 8 million, &c. 07 0,070 read 70 billion, 70 million, &c. 0,8 0 0 read 800 bill'n, 800 mill'n, &c. 6 000 00 0 0 0 read 6 bill'n, and 600 thousand. 56.9 0 0,00 0,00 0,0 0 9 read 900 billion and 9. 57. By canceling' all the ciphers in the last example the 900 billion and 9 becomes only 99. 58. Hence be careful to fill all vacant places 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 m 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 smaller 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. ENGLISH METHOD OF NUMERATING. Hundred thousand quadrillions. Ten thousand quadrillions. Hundred thousand trillions. Hundred thousand billions. Hundred billions. Ten billions. CBILLIONS. Hundred thousand millions Hundred thousands Read 333 thousand 333 quadrillion, 333 thousand 333 trillion, 333 thousand 333 billion, 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 place to each figure; which, if it correspond with the given number is correctly written. NUMERATION TABLE C Hundred Octillions. Hundred Quintillions. Ten Quintillions. Ten Trillions. Hundred Billions. Hundred Millions. Hundred Thousands Tens.-10 "UNITS 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. 38. 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. 3 NUMERALS. Of or belonging to number; consisting of numbers. 6 EUPHONY, [G. eu, good, and phone, sound.] An agreeable sound. 7 PREFIX. Á 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, &o 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 (5) 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 |