49. This method of numeration groups the successive orders into periods of three figures each. The periods are commonly separated by commas, each period taking the name of its lowest order, as shown in the following ORDERS OF UNITS IN THE PERIODS. Hundreds Hundreds Units Hundreds Hundreds - Units ∞ Tens Hundreds Units Quadrillions. Trillions. Billions. Millions. Thousands. Units. 3 0,2 9 1,04 0,0 27,30 6,400 The number is read 30 quadrillion, 291 trillion, 40 billion, 27 million, 306 thousand, 400. 1. In reading numbers, the name of the units period is omitted. 2. Every period except the highest must contain three figures. 50. The names of the periods above Quadrillions are: The fourth, is read, 33 million 300 thousand 330. The diagram may be prepared at first for only two or three periods, and may be gradually enlarged to five or six periods. Each pupil may be allowed to dictate an example, to be written and read by the whole class. 52. RULE FOR NOTATION.-Begin at the left, and write the hundreds, tens, and units of each period in their proper order, filling all vacant places and periods with ciphers. 53. RULE FOR NUMERATION.-I. Begin at the right, and separate the number into periods of three figures each. II. Begin at the left, and read each period as if it were units, giving its name. EXERCISES IN NOTATION AND NUMERATION. 54. Write in figures and read: 1. Six units of the 3d order, five of the 2d, and four of the first. 2. Five units of the 4th order, seven of the 2d, and six of the 1 3. Eight units of the 4th order and four of the 2d. 4. Five units of the 4th order and eight of the 2d. 5. Three units of the 5th order, six of the 4th, four of the 3d, and seven of the 1st. 6. Two units of the 6th order, four of the 5th, nine of the 4th, three of the 3d, and five of the 1st. 7. Three units of the 9th order, eight of the 7th, four of the 6th, six of the 5th, and nine of the 1st. 55. Write and read the following numbers in figures: 1. Twenty-five units in the 2d period, and four hundred ninety-six in the 1st. Ans. 25,496. 2. Four hundred thirty-six units in the 4th period, twelve in the 3d, one hundred in the 2d, and three hundred and one in the 1st. 3. Eighty-one units in the 5th period, two hundred and nineteen in the 4th, and fifty-six in the 2d. 4. Nine hundred and forty units in the seventh period, eighteen in the fifth, and one hundred and three in the 3d. 56. Express the following numbers by figures: 1. Twenty-six thousand twenty-six. 2. Fourteen thousand two hundred eighty. 3. One hundred seventy-six thousand. 5. Seven million thirty-six. 6. Five hundred sixty-three thousand four. 7. One million ninety-six thousand. 8. Ten million ten thousand ten hundred ten. 9. Four hundred eighty-three million eight hundred sixteen thousand one hundred forty-nine. 10. Ninety-nine billion thirty-seven thousand four. 55. Roman Notation employs seven capital letters to express numbers. Thus, Letters. I, V, X, L, C, D, M. Values. 1, 5, 10, 50, 100, 500, 1000. When used alone, each letter has its fixed value. Numbers may be expressed by combining these letters according to the following principles: 1. Repeating a letter repeats its value. Thus, XX represents 20; CCC, 300; DD, 1000. 2. When a letter is placed after one of greater value, its value is to be added to that of the greater. Thus, VI represents 6; XV, 15; LXX, 70; DC, 600. 3. When a letter is placed before one of greater value, its value is taken from that of the greater. Thus, IV represents 4; IX, 9; XL, 40; XC, 90. 4. When a letter of any value is placed between two letters, each of greater value, its value is taken from the sum of the other two. Thus, XIV represents 14; LIX, 59; CXL, 140. 5. A bar or dash placed over a letter increases its valuo one thousand times. Thus, X represents 10000; XC, 90000; DL, 550000. MDCCCLXXX = 1880, one thousand eight hundred and eighty. EXERCISES. 56. Express by Roman notation : 1. Twenty-seven. 2. Forty-nine. 3. Seventy-three. 4. Sixty-eight. 5. Eighty-four. 6. Ninety-seven. 14. 796. 8. Five hundred fifty. 57. Express by Arabic notation: 15. 1069. 16. 25000. 17. 59300. 18. 87040. 1. LXVII. 6. DCLIII. | 11. LIXCCCXLIV. 2. XCLXIV. 7. CXCIX. 12. XVDCCXLIX. 3. CXXXV. 8. VDLIX. 13. MMMMXC. 4. CCXLIX. 9. DLX. 5. MXIX, 14. VMDCCXLIX. 10. XXXID. 15. MDXXVCDLXXXIX. |