The number which any figure expresses when it is con. sidered alone, is called its simple value. The number it expresses when placed with other figures, is called its lo. cal value.

EXERCISES.

Write one ten.—Why is the cipher used ? What would the number be, if the cipher were removed ?

Write one ten and one unit. What is the name of this number? Ans. Eleven.

Write one ten and two units. What is the name of this number?

Write one ten and three units. What is the name ? Write one ten and four units. What is the name? Write one ten and five units. What is the name? · Write one ten and six units. What is the name ? Write one ten and seven units. What is the name? Write one ten and eight units. What is the name? Write one ten and nine units. What is the name ? Write two tens. What is the name ? Ans. Twenty. Write three tens. What is the name ?

Write four tens ; five tens; six tens ; seven tens ; eight tens ; nine tens; and tell their names.

Write one of the order of hundreds.

Write two of the order of hundreds; one of the order of tens ; and four of the order of units.

Write two of the order of hundreds ; no tens ; four units.

Write four hundreds, no tens, nounits.

Write two hundreds, eight tens, and nine units. Seven hundreds, six tens, and three units. Two tens, and two units. Nine tens, and six units. Four hundreds, six tens, and four units. Five hundreds, five tens, and five units. Nine hundreds, seven tens, and three units. Four hundreds, eight tens, and four units. Eight hun. dreds, nine tens, and nine units. Two hundreds, six tens, and three units. One hundred, two tens, and three

What is the simple, and what the local value of figures ? When 2 is considered alone; what is its simple value? When it is written with two figures at the right, what is its local value ?

units. Two hundreds, five tens, and seven units. One ten, and three units. Seven tens, and three units. Nine hundreds, nine tens, and nine units.

In reading numbers, we can either mention each order separately, or simply mention the names of the numbers. I

Thus we can call this number, (21) either two tens, and one unit, or twenty-one.

This number (305) can be read, 3 hundreds ; 0 tens ; 5 units; or it can be called three hundred and five.

The following numbers are read both ways, thus :
10 One ten; no units ; or ten.
11 One ten; one unit ; or eleven.

208 Two hundreds ; no tens ; eight units ; or two hun. dred and eight.

40 Four tens; no units; or forty. Let the pupil read the following numbers both ways.

111. 203. 41. 37. 542. 1. 11. 12. 60. 300. 101. 639. 700. 305.

In this number, (203) why is the cipher put in? What would the number be if it were left out ?

In numeration, every unit of one order, is considered as composed of ten units of a lower order; just as in the coins of this country, ten units of the order of cents, make one unit of the order of dimes, and ten units of the order of dimes, make one unit of the order of dollars.

So in numeration, ten units of the order of units, make one ten; ten units of the order of tens, make one unit of the order of hundreds ; ten hundreds make one unit of the order of thousands ; ten thousands make one of the order of tens of thousands ; ten tens of thousands, make one of the order of hundreds of thousands ; ten hundreds of thousands, make one of the

order of millions, &c. Wherever there are nine units of any order, if there is another added, the number becomes one unit of the next higher order.

If we had nine cents, and should add another, instead of

a

What two ways of reading numbers are there? Give an example. How many units of one order make one unit of a higher order? If one unit is added to nine units of any order, what do they become ?

calling the amount ten cents, we could call it one dime ; and so when ten units are added together, we can call them one unit of the order of tens, instead of ten units of the unit order; and when we have ten units of the order of tens, we can call them one unit of the order of hundreds.

EXERCISES. If nine cents have one more added, in what order do they become a unit ?

If nine dimes have another added, in what order do they become a unit ?

Ten units of the order of dollars, make one unit of what order ?

Ten tens, make one unit of what order ?
Ten units, make one unit of what order?
Ten hundreds make one unit of what order?
The following are the names of the orders.
First order,

Units.
Second order,

Tens.
Third order,

Hundreds.
Fourth order,

Thousands.
Fifth order,

Tens of thousands.
Sixth order,

Hundreds of thousands.
Seventh order,

Millions.
Eighth order,

Tens of millions.
Ninth order,

Hundreds of millions.
Tenth order,

Billions
Eleventh order, Tens of billions.
Twelfth order,

Hundreds of billions.
Thirteenth order,

Trillions.
Fourteenth order, Tens of trillions.
Fifteenth order, Hundreds of Trillions.
Sixteenth order, Quadrillions.
Seventeenth order, Tens of Quadrillions.
Eighteenth order, Hundreds of Quadrillions.
Nineteenth order, Quintillions.
Twentieth order, Tens of Quintillions.

What are the names of the orders ? If a figure 2 stands in the first order, what number does it express ? What number does it express, if it stands in the fourth order? In the second order ? In the fifth order ? In the sixth ? seventh ? eighth ?

Twenty-first order, Hundreds of Quintillions.

Twenty-second order, Sextillions. Sextillions are as high as there is ordinarily any need of writing or reading.

In all the above orders, “ Ten units of one order, make one unit of the next higher order. Let the pupil write the following

EXERCISES. 1. Five units.

21. Five tens and two units. 2. Three tens; two units.

22. Five hundreds. 3. Thirty-two.

23. Five tens. . 4. Three and ten, or thirteen. 24. Fifty. 5. Four and ten.

25. Five hundred, and five units. 6. Four tens, or forty.

26. Five and ten. 7. Six and ten.

27. Fifteen. 8. Six tens.

28. Fifty-seven. 9. Sixteen.

29. Four hundreds, six tens. 10. Sixty.

30. Four hundred and sixteen. 11. One hundred and sixteen. 31. Four hundreds, one ten, and six. 12. One hundred, one ten, and six. 32. Four hundred, and six. 13. One hundred and sixty.

33. Two hundred and sixty-six. 14. One hundred, and six tens. 34. Three hundred, ten, and one. 15. Two hundred, two tens.

35. Three hundred and eleven. 16. Two hundred and twenty. 36. Three hundred, ten, and two. 17. Two hundred and thirty. 37. Three hundred and twelve. 18. Two tens and two units.

38. Four hundred and one. 19. Twenty-two.

39. One hundred and forty-two. 20. Two hundreds and two units. 40. Two hundreds, two tens. Let the pupil write the following

EXERCISES. 1. One unit of the fourth order. What number is it? Which orders have ciphers in them?

2. Two units of the fourth order; one unit of the sec. ond order, and one unit of the first order. What number is it? What order has a cipher in it?

3. Two thousands; one hundred ; five tens ; six units. 4. Twenty-one hundreds ; five tens ; six units. Is there any difference between the two last numbers ?

5. Three thousands, four hundreds, six tens and three units.

6. Thirty-four hundred, and sixty-three.
Is there any difference in the two last numbers?
7. Three thousands and three units.
Which orders have ciphers placed in them?

8. Three thousands, six hundreds.
Which orders have ciphers placed in them ?
9. Thirty-six hundred.
What two ways of reading this last number?
10. Twenty thousand.
11. Two tens of thousands.

Is there any difference between these two last num. bers ?

12. Twenty-four thousand.
What two ways of reading this last number?

13. One hundred thousand, two tens of thousands, five thousands, six hundreds, four tens, and three units.

14. One hundred and twenty-five thousand, six hun. dred and forty-three.

Is there any difference between these two last num. bers ?

15. Two tens of thousands, one thousand, four hun. dreds, six tens, five units.

What two ways of reading this number?

16. Four hundred and sixty-two thousand, five hundred and six.

What two ways of reading this last ? 17. Forty-four thousand, four hundred and forty-four. What two ways of reading this last ?

18. Four hundreds of thousands, five thousands, six hundreds, two tens, five units.

What two ways of reading this last number? 19. 'Two hundred thousand, two thousand, two units. What orders have ciphers placed in them? 20. Twenty thousand, and two units.