22. The numbers between ten and twenty are repre

sented by writing 1 in the second place and the units in

The words thir-teen, four-teen, etc., mean three and ten, four and ten, etc.

23. In like manner the numbers between 20 and 30, are represented by writing the tens in the second place, and the units in the first place. Thus,

Twenty-one 21 Twenty-four 24 Twenty-seven 27 Twenty-two 22 Twenty-five 25 Twenty-eight 28 Twenty-three 23 Twenty-six 26 Twenty-nine 29

Write in figures and arrange in columns :

7. Three tens and six units, seven tens and five units,

four tens and three units, and eight tens.

8. The numbers between forty and fifty.

9. The numbers between seventy-five and eighty-six. 10. The numbers between eighty-two and ninety-four.

11. Twelve, twenty-five, fifty-seven, thirty-four, sixtytwo, forty-nine, seventeen.

12. Forty-six, sixty-eight, forty-nine, ninety.

24. The greatest number that can be represented by two figures is 99.

25. By grouping ten units of the second order or ten tens into a larger collection, there is formed a unit of the third order, called a hundred, which is represented by writing the figure 1 in the third place with two ciphers after it; thus, 100.

26. In like manner are represented

27. The numbers from one hundred to nine hundred ninety-nine are represented by writing the hundreds in the third place, the tens in the second place, and the units in the first place. Hence

28. Orders of Units are denoted by the position of the figures used in expressing a number.

Thus, 426 represents 6 units of the first order, 2 units of the second order, or 2 tens, and 4 units of the third order, or 4 hundreds, and is read four hundred and twenty-six.

29. PRINCIPLES 1. Ten units of any order in a number make one unit of the next higher order.

2. When any order of units in a number is vacant, fill the place with a cipher.

EXERCISES.

30. Copy and read the following and name the num

ber of hundreds, tens, and units in each.

Write in figures and arrange in columns :

6. Seven hundred five tens two units, three hundred six tens eight units, five hundred seven units.

7. The numbers between two hundred and twenty-eight, and two hundred and thirty-four.

8. The numbers between four hundred and ninety-six, and five hundred and seven.

9. One hundred and sixty-five, three hundred and forty, seven hundred and eighty-one, and nine hundred and seventy-four.

31. The greatest number that can be expressed by three figures is 999.

32. By grouping ten units of the third order, or ten hundreds into a larger collection, there is formed a unit of the fourth order called a thousand, which is represented by writing the figure 1 in the fourth place with three ciphers after it; thus, 1000.

33. In like manner are represented : Two thousand by 2000

"3000

Six thousand

by 6000

Three thousand

34. The numbers from one thousand to nine thousand nine hundred and ninety-nine, are represented by writing thousands in the fourth place, hundreds in the third place, tens in the second place, and units in the first place.

Thus, 3508 represents 8 units of the first order, 0 units of the second order, or no tens, 5 units of the third order, or 5 hundreds, and 3 units of the fourth order, or 3 thousands, and is read three thousand five hundred and eight.

EXERCISES.

35. Copy and read the following, naming the number of units of each order.

6. Three units of the fourth order, five units of the third order, two units of the second order, and one unit of the first order.

7. Six units of the fourth order, eight of the second order, and four of the first order.

8. Nine units of the fourth order, four units of the second order, and seven of the first order.

9. One thousand three hundred and forty-seven. 10. Five thousand six hundred and seventeen.

11. Four thousand nine hundred and ten.

12. Eight thousand and seventy-nine.

13. Nine thousand six hundred and twelve.

14. Six thousand six hundred and six.

15. Nine thousand nine hundred and nineteen. 16. Seven thousand and seventy-eight.

17. Five thousand two hundred and five. 18. Eight thousand eight hundred and ten.

19. Nine thousand three hundred and fifteen.

36. The greatest number that can be expressed by four figures is 9999.

37. In the same manner other new orders are formed to represent larger numbers, by grouping ten units of the fourth order to form the fifth order, or tens of thousands; and ten units of the fifth order to form the sixth order, or hundreds of thousands; and ten units of the sixth order to form the seventh order, or millions, etc.

Thus, 263045 represents 5 units of the first order, 4 units of the second order, or 4 tens, 0 units of the third order, or no hundreds, 3 units of the fourth order, or 3 thousands, 6 units of the fifth order, or 6 tens of thousands, and 2 units of the sixth order, or 2 hundreds of thousands, and is read two hundred sixty-three thousand and forty-five.

38. The value of any order of units is increased tenfold for every place it is moved from the right to the left.

39. The value of any order of units is diminished tenfold for every place it is moved from the left to the right.

40. A Scale in numbers, is a succession of units, increasing and decreasing according to a certain law, or rule. Scales are uniform or varying.

41. A Decimal Scale is one in which the law of increase and decrease is uniformly TEN. Hence, Arabio Notation has a decimal scale.