39. The fourth group of three orders or places from the right is called the Period of Billions.

412123000000 is composed of 412 billions 123 millions, or of four periods, and is read 412 billion 123 million.

90000050000 is composed of 90 billions 50 thousands, or of four periods, and is read 90 billion 50 thousand.

40. The names of the Orders of Units and the names of the Periods are given in the following

This number is read 400 quadrillion 40 trillion 4 billion 444 million 440 thousand 404.

The Periods above Quadrillions are Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecib lions, Octodecillions, Novendecillions, Vigintillions, &c.

PRINCIPLES OF NUMERATION AND NOTATION.

41. FIRST. Ten units of any order in a number" are always equal to one unit of the next higher order.

SECOND. Removing a figure one place to the left, increases its value tenfold. Removing a figure one place to the right, diminishes its value tenfold.

THIRD. The name and value of the units represented by a figure in a number are always those of its order in that number.

FOURTH. The absence of units in any order in a number is denoted by a cipher.

RULES FOR NUMERATION AND NOTATION.

42. NUMERATION.-Beginning at the right, separate the numbers into periods of three figures each. Then read the number in the first period at the left, adding the name of the period; do the same with each period in order toward the right, omitting to name the units period and any period or periods composed only of ciphers.

NOTATION.-Beginning at the left, write the hundreds, tens, and ones of each period in their proper order, filling all vacant orders and periods with ciphers.

Write the following numbers in figures:

1. Twenty-two thousand seven hundred sixty-five. 2. Eighty thousand two hundred one.

3. Thirty thousand thirty.

4. Four hundred ten thousand two hundred five. 5. Ninety thousand one.

6. Eight hundred thousand six hundred sixty-nine.

7. Nine hundred thousand one.

8. Five hundred thousand fifty.

9. One hundred million ten thousand one. 10. Ninety-one million seven thousand sixty. 11. Seventy million four.

12. Seven hundred million ten thousand one. 13. One billion one million forty.

14. Forty billion two hundred thousand five.

15. Seven hundred twenty-six billion fifty million one thousand two hundred forty-three.

ROMAN NOTATION.

43. In the Roman Method numbers are expressed by means of seven characters.

44. The Roman method of expressing numbers had its origin in Rome.

45. The Characters used in this system of expressing numbers are seven Letters.

46. The letters used are the following:

47. When used alone each letter has a fixed value.

48. When a letter is repeated, its value is repeated. Thus, III are 3, XX are 20, CCC are 300, MM are 2000.

49. When a letter follows one of greater value, their sum is the number expressed. Thus, VI are 6, LX are 60.

50. When a letter precedes one of greater value, their difference is the number expressed. Thus, IV are 4, XL are 40.

51. When a letter is placed between two others of greater value, the difference between it and their sum is the number expressed. Thus, XIX are 19, XIV are 14.

52. When a horizontal line is placed over a letter, its value is increased a thousand times. Thus V is 5000.

53. Uses.-Roman notation is not convenient for arithmetical computations, but is used principally in marking dials, numbering chapters, sections, &c., in books, and in writing physicians' prescriptions.