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PRACTICAL ARITHMETIC.

1. A unit is a single thing, or one.

One man, one dollar, one regiment, one, are units.
2. A number is a unit, or a collection of units.

Three men, five dollars, nine regiments, are numbers.

3. An abstract number is a number the name of whose unit is not given.

Seven, fifteen, forty-five, one hundred six, are abstract numbers.

4. A concrete number is à number the name of whose unit is given.

Six horses, nine pounds, ten dollars, are concrete numbers.

5. A simple number is a number which expresses one or more units of the same name or denomination; as, 5 yards; 3 dollars; 7.

6. A compound (or denominate) number is a number containing units of two or more different names or denominations, but the same in kind; as, nine pounds twelve ounces; and five bushels three pecks two quarts.

7. Arithmetic teaches the use of numbers.

NOTATION AND NUMERATION.

8. Notation is the writing of numbers with figures, or with letters.

9. Numeration is the reading of numbers expressed by figures, or by letters.

10. Figures are not numbers, but characters or marks that represent numbers.

20. Read and explain the meaning of the following:

1. 11; 14; 13; 12. |4. 107; 207; 680. 2. 17; 19; 26; 38. 5. 362; 359; 475. 3. 51; 68; 94; 99.16. 520; 811; 120.

7. 808; 497; 305.

8. 642; 85; 900. |9. 729; 902; 999.

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18. Three hundred thirty-three; three hundred three. 19. Seven hundred seventeen; seven hundred seventy. 20. Eight hundred eighty; eight hundred eighteen. 21. Nine hundred nine; nine hundred ninety-nine.

22. Read the following, showing that the value of a figure is made ten times as great by moving it one place to the left.

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Thus: 1 is 1 unit; 10 is 1 ten or 10 units; 100 is 1 hundred, 10 tens, or 100 units; 111 is 1 hundred, 1 ten, and 1 unit, or one hundred eleven.

23. The three places, hundreds, tens, and units, constitute a period.

24. The largest number expressed by one figure is 9, by two figures, 99; and, by three figures, or the first period, 999.

25. To write ten hundred, write 10 with two ciphers (1 with three ciphers) at the right, thus, 1000; it is read ten hundred, or one thousand.

18. A number may contain units of two or more orders.

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104, one hundred four; 560, five hundred sixty; 789, seven hundred eighty-nine.

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19. 1. In 111 what does the 1 in the first or right-hand place stand for? The 1 in the second place?

third or left-hand place?

The 1 in the

2. What does 63 stand for? 91 ? 125? 152 ? 523 ? 600 ? 900 ?

3. In 218 how many hundreds are there? How many tens? How many units?

4. How many hundreds, tens, and units are there in 289 ? In 476? In 418? In 801 ? In 760 ? In 927 ?

20. Read and explain the meaning of the following:

1. 11; 14; 13; 12. 14. 107; 207; 680. 2. 17; 19; 26; 38.5. 362; 359; 475. 3. 51; 68; 94; 99.16. 520; 811; 120.

7. 808; 497; 305. 8. 642; 85; 900. 9. 729; 902; 999.

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18. Three hundred thirty-three; three hundred three. 19. Seven hundred seventeen; seven hundred seventy. 20. Eight hundred eighty; eight hundred eighteen. 21. Nine hundred nine; nine hundred ninety-nine.

22. Read the following, showing that the value of a figure is made ten times as great by moving it one place to the left.

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Thus: 1 is 1 unit; 10 is 1 ten or 10 units; 100 is 1 hundred, 10 tens, or 100 units; 111 is 1 hundred, 1 ten, and 1 unit, or one hundred eleven.

23. The three places, hundreds, tens, and units, constitute a period.

21. The largest number expressed by one figure is 9, by two figures, 99; and, by three figures, or the first period, 999. 95. To write ten hundred, write 10 with two ciphers (1

ce ciphers) at the right, thus, 1000; it is read ten ? one thousand,

26. The fourth place expresses thousands; it is the place of the lowest, or units' order, in the second period, or period of thousands.

27. 1. Beginning at the right, the first three places, units, tens, and hundreds, form, the first period or the period of units.

2. The three places of the second group, towards the left, are also named units, tens, and hundreds, and they form the second period or the period of thousands.

3. The three places of the third group are also named units, tens, and hundreds, and they form the third period or the period of millions.

4. Each group of three places, units, tens, and hundreds, towards the left, is a separate period, the names of other periods, in their order being: billions, trillions, quadrillions, quintillions, sextillions, septillions, octillions, nonillions, decillions, etc.; as in the following:

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The first of the above numbers is read: four hundred five billion, six

hundred twenty-one million, five hundred seventy thousand, six hundred thirty-two.

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