21. Ninety-nine is the largest number which can be ex pressed by two figures.

22. To express the numbers from ninety-nine to one thou sand, requires three figures written side by side.

23. The figure in the third place denotes ten tens, which are called Hundreds, or Units of the Third Order.

Thus, the figures 436, denote 4 hundred, 3 tens, and 6 units, and are read, "Four hundred thirty-six."

Write the following numbers in figures:

29. Two hundred forty-six. 33. Five hundred eight. 30. Three hundred fifty-four. 34. Six hundred seventy. 31. Five hundred thirty-two. 35. Eight hundred three. 32. Four hundred fifty.

Read the following numbers :*

36. Nine hundred ninety-nine.

24. Nine Hundred Ninety-nine is the largest number expressed by three figures.

* In reading numbers expressed by three or more figures, omit the word and after hundreds.

25. To express larger numbers, other orders of units are formed, called thousands, ten-thousands, hundred-thousands, millions, etc.

26. A figure in the fourth place denotes Thousands, which are called Units of the Fourth Order.

27. A figure in the fifth place denotes Ten-thousands, which are called Units of the Fifth Order.

28. A figure in the sixth place denotes Hnndred-thousands, which are called Units of the Sixth Order.

29. A figure in the seventh place denotes Millions, which are called Units of the Seventh Order.

30. If any orders are omitted, ciphers must be written in their places.

Thus, four thousand three hundred five, is written 4305.

The figures 5046, denote 5 thousands, 0 hundreds, 4 tens, and 6 units, and are read, "Five thousand forty-six."

Write the following in figures:

53. Three thousand two hundred sixty-eight.

54. Five thousand seventy-five.

55. Six thousand three hundred ten.

56. Seven thousand fifty-three.

57. Eight thousand seven hundred five.

58. Nine thousand nine hundred, ninety-nine.

31. The different values of units expressed by the significant figures, are determined by the place they occupy, and are called simple and local values.

32. The Simple Value of the units represented by the sig nificant figures is the number which they represent when standing alone or in units place.

33. The Local Value of these units is the number which they represent when standing on either side of units place.

Thus, 2 standing alone, or in the first place, denotes 2 simple unito; in the second place, it denotes 2 tens, as in 25; in the third place, it denotes 2 hundreds, as in 246, etc.

NOTE. These different orders of units correspond to dollars, dimes, and cents. Thus, 10 cents make 1 dime, 10 dimes 1 dollar. Now a cent is a unit, a dime is a unit, and a dollar is a unit; but these units have different values, corresponding to the orders of units.

34. From the above illustrations we derive the following

PRINCIPLES.

1°. Ten units of any order make a unit of the next higher order.

2°. Moving a figure one place to the left, increases its value

ten times.

3°. Moving a figure one place to the right, diminishes its

value ten times.

35. Hence, the great law of the Arabic Notation, viz.:

The Orders of Units increase and decrease by the uniform scale of Ten.

The Arabic Notation is therefore called the Decimal System, from the Latin word decem, which means tene

36. To Express Decimal Parts of a Unit.

By the law of the decimal notation a unit of the third order is ten times a unit of the second order; a unit of the second order is ten times a simple unit or one.

By extending this law below units, a simple unit is ten times a unit of the first decimal order; a unit of the first decimal order is ten times a unit of the second decimal order, and so on. In this way a series of orders is formed below units which regularly decrease by the scale of ten.

37. The first order on the right of units is called tenths; the second, hundredths; the third, thousandths; etc.

38. These lower orders are separated from units by a period. (.) called the Decimal Point.

39. The orders on the left of the decimal point are called Whole Numbers or Integers; those on the right, Decimals.

Thus, seven and five tenths are written 7.5; nine and fifty-three hundredths are written 9.53; sixty-five and two hundred seventy-three thousandths are written 65.273. The figures 4.7 denote four ones and seven tenths of one, and are read, "Four and seven tenths." The figures 6.35 denote six ones and thirty-five hundredths of one, etc.

40. The French Method of writing and reading large numbers, is shown in the following

41. The first period on the left of the decimal point expresses units, tens, and hundreds, and is called Units Period; the second period denotes thousands, etc., and is called Thousands Period; and so on.

42. Beginning at unit's place, the orders on the right of the decimal point express tenths, hundredths, thousandths, etc.

The number in the table is read, "Six hundred fifty-one trillions, seven hundred eighty billions, nine hundred millions, two hundred forty thousand, seven hundred eighty-five, and three hundred twenty-four thousandths."

43. To express larger numbers, other periods are formed in like manner, called Trillions, Quadrillions, Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, etc.

44. To Express Numbers by Figures:

Begin at the left and write the figures of the given orders in succession towards the right. If any orders are omitted, supply their places by ciphers, and separate tenths from units by a decimal point.