Fifty thousand two hundred two, or 5 ten-thousands 2 hundreds 2 units, is written 50,202.

Five hundred fifty-five thousand two hundred twentytwo, or 5 hundred-thousands 5 ten-thousands 5 thousands 2 hundreds 2 tens 2 units, is written 555,222.

1. Six units of the fifth order, with seven units of the third order.

Ans. 60,700; read, sixty thousand seven hundred.

2. 3 hundred-thousands 4 ten-thousands 4 thousands. Ans. 344,000; read, three hundred forty-four thousand.

3. Two units of the fourth order, with three units of the second order.

4. Eight units of the fifth order, with three units of each of the lower orders.

5. 9 units of the sixth order, with no units of the fifth order, and six units of each of the lower orders.

6. 316 in the second period, 0 in each order of the first period.

7. 21 thousands 2 tens and 1 unit.

8. 2 hundred-thousands 5 ten-thousands with five units of the third order.

9. The greatest number that can be expressed by three figures.

10. The greatest number that can be expressed by six figures.

REVIEW.-What are ten tens called? (25.) Ten hundreds? (27.) Ten thousands? (28.) Ten ten-thousands? (29.) Name the first six orders. (30.) The first two periods. (80.)

ΝΟΤΑΤΙΟΝ.

32. Notation is the method of writing numbers.

The method of expressing numbers by figures is called the Arabic, because it was used by the Arabs.

33. The Periods are named from the right; thus, Units, thousands, millions, billions, trillions, etc. The Orders are named from the right; thus,

UNITS, tens, hundreds; THOUSANDS, ten-thousands, hundred-thousands; MILLIONS, ten-millions, hundred-millions; BILLIONS, ten-billions, hundred-billions; TRILLIONS, tentrillions, hundred-trillions, etc. Hence the following

where the figures express five hundred sixty-two TRILLION, seven hundred ninety-three BILLION, one hundred fifty-four MILLION, two hundred five THOUSAND, six hundred and thirty-eight.

What is Notation? What is the method of expressing numbers by figures called? Why so called? Name the Periods from the right. Name the Orders. State the Orders in the table.

of

The periods above TRILLIONS, in their order, are QUADRILLIONS, QUINTILLIONS, SEXTILLIONS, SEPTILLIONS, etc.

PRINCIPLES OF NOTATION.

34. 1. Ten units of any order are always equal to one of the next higher.

For ten units are one ten, ten tens are one hundred, ten hundreds are one thousand, and so on. Hence,

2. Each removal of a figure an order towards the left makes the value expressed ten-fold.

For the value of the units expressed by a figure is determined by the order occupied by the figure.

WRITTEN EXERCISES.

35. 1. Write in figures, seven million six hundred ninety-three thousand two hundred four.

Writing the 7 millions as the only order of the third period, 693 thousands as the orders of the second period, and 204 as the orders of the first period, we have 7,693,204. Hence, the following

Rule.- Beginning with the highest period to be expressed, write the figures belonging to each period, in their orders, and observe to mark the omission of any order of units with a cipher.

What periods are above Trillions? How many units of any order are always equal to one of the next higher? How is the value expressed increased by each removal of a figure toward the left? Recite the Rule for Notation.

Examples.

Write in figures the following numbers:

2. Seven hundred seventy.

3. One thousand eight hundred eighty-five.

4. Three thousand five hundred fifty-three.
5. Eleven thousand one.

6. Eleven hundred eleven.

7. Seventy-three thousand five hundred ninety-two. 8. Eighty-four thousand nine hundred nine.

9. Two hundred thirty thousand five hundred six. 10. Forty-one thousand nineteen.

11. Nine thousand nine hundred seven.

12. Eighty-nine thousand ninety-seven.

13. Twenty-one thousand one hundred twenty-one. 14. Three hundred thousand six.

15. Fifteen thousand one hundred fifteen.

16. Seventy-nine thousand nine hundred seven. 17. Sixty-seven thousand three hundred six.

18. Six hundred thirty-five thousand four hundred thirty-eight.

19. Forty-two thousand four hundred forty-four.

20. Ninety-eight thousand six hundred nine.

21. Nineteen thousand three hundred fifty-one. 22. One hundred thousand forty-seven.

23. One million ten thousand ten.

24. Sixty-one million sixteen thousand six hundred five.

25. Eight hundred twelve thousand three hundred forty-seven.

What is an Example? Ans. A question, or something to be done, under a rule.

26. Twelve million twenty thousand three hundred one. 27. Seven million nine hundred twenty-three thousand four hundred six.

28. Three billion one hundred eleven million two hundred twenty thousand two.

29. Five hundred eighty-one million thirty-six thousand twenty-nine.

30. One trillion one million one thousand ninety-one. 31. Twenty-nine million fifty thousand one hundred fifty.

32. One hundred million one hundred thousand one hundred one.

33. Six hundred thirty-one million one hundred twentyfour thousand sixty-six.

34. Five trillion five thousand five.

35. Two hundred ninety trillion six hundred thirty billion four hundred two million four hundred seventynine thousand eight hundred fifteen.

NUMERATION.

36. Numeration is the method of reading numbers.

WRITTEN EXERCISES.

37. Let it be required to read 7693254.

Pointing off the given figures into periods, from the right, we have 7,693,254.

REVIEW. What is an Operation? (13.) What is a Rule? (14.) What is the cipher sometimes called? (18.) What do ciphers written with other figures denote, as in 108, 240, etc.? Ans. Vacant orders, or such as have an omission of units.