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If we place figures at the right of units, we can denote tenths, hundredths, &c., as in the following table. The numbers so written are called DECIMALS; and to distinguish them from whole numbers, they are separated from units by a dot, called the Decimal Point, or Separatrix.

Hundred millions.
Ten millions.

Hundred thousands.
co MILLIONS.

Ten thousands.

THOUSANDS.
Hundreds.

Hundred thousandths.
MILLIONTHS.

Ten thousandths.

Hundredths.

THOUSANDTHS.

Ten millionths.
Hundred millionths.

UNITS.
Tenths.

Tens.

5 6 3, 2 7 9, 5 4 1.4 5 9 7 2 3 6 5.

The above number is read, Five hundred and sixty. three million, two hundred and seventy-nine thousand, five hundred and forty-one-and forty-five million, nine hundred and seventy-two thousand, three hundred and sixty-five hundred millionths.

The character 0, as its name denotes, has no value by itself, but is employed when there are none of the denomination whose place it occupies. Thus, in 106 there are 0 tens; in .004 there are no tenths or hundredths. On this account, Os at the right of decimals or at the left of whole numbers, do not affect their value.

Examples to be Read and Explained by the Teacher on the Board. 2,005,016.0003006 201,897.049003

Teach the pupil to place a comma at each third figure to the right and to the left of the decimal point, as in the example below. Then the first period of integers will represent units; the second thousands; the third millions, &c. The first decimal period will represent thousandths; the second millionths, &c. He may also commence with the right hand decimal

figure, and place a supplementary comma above each third figure to the left. He will then soon perceive that

97,000,006.01'3,70'6,95

is read, Ninety-seven million and six,-and one million, three hundred and seventy thousand, six hundred and ninety-five, hundred millionths.

Examples to be Written on the Slate, and Read by the Pupil.

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43. Repeat the Numeration Table, for whole numbers and decimals.

Examples to be Written and Explained by the Teacher on the Board.

Twenty-nine million and sixteen,-and forty-three thousand and four ten millionths.

Four hundred million, forty thousand and four,-and seven thousand and six hundred millionths.

Show the pupil, that in whole numbers the highest denomi nation is first written, and that the units, tens and hundreds of each succeeding denomination must occupy at least three places, the deficiency (when there is any,) being supplied by Os. Decimals should be written as whole numbers, and Os should then be prefixed, if necessary, until the right-hand decimal figure represents the denomination required.

Examples to be Written in Figures, and Numerated by the Pupil.

1. Ninety.

2. Sixty-four.

3. Eighty-seven-and one, tenth.

4. Sixteen-and four, hundredths.

5. Seven hundred-and nineteen, hundredths.

6. Three hundred and two.

7. Five hundred and ninety-and eleven, thousandths.

8. Six hundred and ninety-nine, ten-thousandths. 9. Two thousand and eight, ten-thousandths. 10. Five thousand-and five, thousandths. 11. Twelve thousand and ninety-and ninety-nine, hundred-thousandths.

12. Ninety-nine thousand nine hundred and ninetynine, millionths.

13. Two hundred-and twenty-eight, millionths. 14. Two hundred and twenty-eight, millionths. 15. Nine hundred and three thousand-and seventeen, ten-millionths.

16. Nine hundred and three thousand and seventeen, ten millionths.

17. Eighty-four thousand and seventeen-and three hundred and nine, ten-thousandths.

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18. Eighty-four and one hundred and seventy thousand three hundred and nine, ten-millionths.

19. Twenty thousand and six-and four hundred and nine, hundred thousandths.

20. Thirty thousand one hundred and two- and four hundred and nine, hundred-millionths.

21. Nine hundred thousand and nine, millionths. 22. Nine hundred thousand and nine, hundredmillionths.

23. Nine hundred thousand - and nine, hundredmillionths.

24. Six hundred and four million six hundred and four-and seventy-three, ten-thousandths.

25. Twenty-eight thousand six hundred and fortytwo-and forty-two, thousandths.

26. One million three hundred and seven thousand and forty and seven hundred and three, ten-millionths.

27. Forty-seven million nine hundred and sixty thousand eight hundred and thirteen, hundred-millionths.

28. Four hundred million—and four, hundred millionths.

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29. Nineteen million and six- and fifteen, tenmillionths.

30. In ninety thousand four hundred and fortythree, hundredths, how many tenths, units, tens, hundreds, &c ?*

31. In two hundred thousand and twenty-one, ten thousandths, how many thousandths, hundredths, tenths, &c.

*The number is written 904.43. Then there are 9044 tenths, 904 units, 90 tens, or 9 hundreds.

6

CHAPTER II.

ADDITION.

EXAMPLE FOR THE BOARD.

A gentleman bought a coat for 21.25 dollars, a vest for 3.00 dollars, and a pair of pantaloons for 5.62 dollars. What did they all cost him?

Tens.

Tenths.

Hundredths.

2 1.2 5

3.0 0

Writing the numbers so that all the units may fall in one column, all the tenths in another, and so on, we add first the right-hand column: 2 hundredths and 0 hundredths are 2 hundredths, and 5 hundredths are 7 hundredths. We therefore write 7 under the column of hundredths. Adding in the same manner the tenths, the units, and the hundreds, we find there are 8 tenths, 9 units, and 2 hundreds. The answer, or sum, is therefore 29.87 dollars.

5.6 2

29.8 7

The sign

signifies dollars. The hundredths of dollars are called cents, and the thousandths of dollars, mills.

1. A merchant sold one barrel of flour for $5.00, one barrel for $5.62, and one barrel for $4.37. How much did he receive for the whole?

2. A gentleman bought a barrel of sweet potatoes for $1.12, a barrel of flour for $5.25, and a barrel of sugar for $18.10. He paid a drayman $0.50 to take them home; how much money did he expend for the whole?

3. What will four bushels of potatoes cost, at $0.32 a bushel?

4. What will be a labourer's wages for five weeks, at $3.11 a week?

5. How many yards of broadcloth are there in three pieces, the first containing 21.35 yards, the second 27.6 yards, and the third 30.03 yards?

6. What is the sum of 28, 10.3, 90.56, and 11.01 ?

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