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16. Express in figures the following:
Three tens and eight units. Five tens and seven units.
Four tens and seven units. Eight tens and one unit.
Two tens and two units. Seven tens and three units.
One ten and three units. One ten and eight units.
Six tens and nine units, Four tens and two units.
Three units of the second order, six of the first order.
Two units of the second order, four of the first order.

Write all the numbers between 10 and 20. Between 30 and 50. Between 70 and 90.

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17. In reading a number expressed by three figures, the tens are read after the hundreds without the word and. Thus, 235 is read two hundred thirty-five instead of two hundred and thirty-five. 18. Read the following: 746 932

786 849 534 678 453 777 391 585 963 378 243 873

412 531 217 918 855 248

19. Express in figures the following:
Two hundreds, three tens, five units.
Six hundreds, two tens, nine units.
Four hundreds, one ten, eight units.
Three units of the third order, six of the second order.
Three hundred eighteen. Seventy
Eight hundred thirty.

Seven.
Four hundred four.

Seven hundred six. Six hundred eighty-one.

Six hundred forty. Seven hundred seventy.

Two hundred six.
Seven hundred.

One hundred eleven.
Seven hundred seventy-seven.

From the previous examples we deduce the following general principles :

20. PRINCIPLES.—1. The representative value of a figure is increased tenfold by each removal one place to the left, and decreased tenföld by each removal one place to the right.

2. The figure 0 is used to give significant figures their positions.

21. In reading numbers a new name is given the order of units next higher than hundreds of any denomination. Thus, the order next higher than hundreds is called thousands, that next higher than hundreds of thousands, millions, etc. Therefore each denomination can have but three orders of units.

22. A Period is a group of figures containing the hundreds, tens, and units of any denomination.

The present system of notation is illustrated by the following

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3 0,2 30,1 6 0,70 0,40 1,6 9 0. This number is read thirty quadrillion, two hundred thirty trillion, one hundred sixty billion, seven hundred million, four hundred one thousand, six hundred ninety.

1. In reading numbers, the name of units' period is omitted.
2. Each period, except the highest, must contain three figures.
3. The periods are separated from each other by commas.

23. The periods above Quadrillions, in their order, are Quintillions, Sextillions, Septillions, etc. 24. Give the number of each of the following periods: Millions.

Trillions.

Billions.
Thousands.

Units,

Quadrillions.
25. Give the names of the following:
5th period.
2d period.

1st period.
3d period.
4th period.

6th period. 26. Repeat in order the names of the periods from: Units to billions.

Billions to units.
Units to quadrillions. Quadrillions to units.
Thousands to trillions.

Millions to thousands.

27. Copy and point off into periods: 1. 46825. 5. 38420058.

9. 5284325684. 2. 239746. 6. 33468204. 10. 7932468512. 3. 180040. 7. 8438206. 11. 83749275867. 4. 14168843. 8. 436784.

12. 1423789276586. 13. How

many

thousands are there in the first number? 14. How many thousands in the second number? 15. How many billions in the next to the last number?

16. How many trillions in the last number? How many billions? How

many
millions? How

many

thousands? How many units?

17. Point off into periods, and name in order, the billions, millions, thousands, and units of the next to the last number.

18. Point off into periods, and name in their order, the periods composing the 12th number.

19. In like manner point off and read each of the numbers.

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28. Write in figures:
1. Thirty-four billion, eighteen thousand, forty.

ANALYSIS.-Since the highest period is bill

ions, which occupy the fourth period, we make sem four spaces for the periods. We write 34 in the

fourth period, thus expressing the billions of 34 000 018 040 the given number; 18 in the second period, thus

expressing the thousands; and 40 in the first

period, thus expressing the units. Since every 34,000,018,040 period except the highest must contain three

figures, we fill the vacant places with ciphers. As soon as possible use commas instead of the lines, and cease to write both the number and name of the periods.

Lions

.

Ora

Ed. od.

S.

Write in figures, and read the number:

2. Thirty-six in the 3d period, two hundred eighteen in the 2d, eight hundred forty-six in the 1st.

3. Eighty-four in the 4th period, five hundred forty in the 3d, six hundred in the 2d, forty in the 1st.

4. Two hundred one in the 5th period, seventy-five in the 4th, five hundred sixty-two in the 3d, twelve in the 2d, one in the 1st.

5. Sixty in the 5th period, four hundred two in the 4th, three hundred thirty-three in the 3d, two hundred in the 2d, one hundred eleven in the 1st.

5684 8512 55867 3586

r!

? any low

Write in figures:

6. Seventy-three million, two hundred fourteen thousand, seventy.

7. Eighty billion, forty million, six hundred twelve thousand, seven hundred eighty-eight.

8. Two hundred twenty-five million, six hundred fortyone thousand, three hundred fifty-one.

9. Three hundred fifty-four billion, six hundred four million, eight hundred ninety-two thousand, thirty-six.

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29. RULE FOR NOTATION.-Begin at the left and write the hundreds, tens, and units of each period in their proper order, putting ciphers in all vacant places and periods.

While writing, separate each period from the next by a comma.

30. RULE FOR NUMERATION.--Begin at the right and separate the numbers into periods of three figures each.

Begin at the left hand and read each period as if it stood alone, adding its name.

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32. Write in figures, and read:
22. Two hundred in the 1st period.
23. Sixty in the 2d period, two in the 1st.
24. Seven hundred in the 3d period.
25. Two hundred thirty in the 3d period, sixty in the 1st.

26. Eighty-one in the 4th period, five hundred one in the 3d, seven in the 2d, twelve in the 1st.

27. Thirty in the 5th period, six hundred three in the 1st. 28. Seven hundred in the 5th period, eighty in the 4th.

29. Eight in the 4th period, seven in the 3d, fourteen in the 2d, and ten in the 1st,

30. Fifteen in the 6th period, eighteen in the 4th, two hundred seven in the 3d, and eighty-one in the 1st.

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