Recite the orders of units, ascending, from simple Units to Decillions. Recite them, descending, beginning with Hundreds.-Beginning with Thousands. Beginning with Tens of thousands. Beginning with Hundreds of thousands. Beginning with Millions. Beginning with Billions.

What are the relative values of these different orders of units? (10.)

ΝΟΤΑΤΙΟΝ.

(12.) NOTATION is the method of denoting numbers by numeral figures.

These figures, sometimes called the digits of numbers, are 1 one, 2 two, 3 three, 4 four, 5 five, 6 six, 7 seven, 8 eight, 9 nine; and 0 zero or cipher, which has no value. O is used to occupy vacant places in Notation.

The Higher Orders of Units denoted.

(13.) The ascending orders of units are denoted by figures in a row, from right to left; the first on the right denotes units, the second tens, the third hundreds; and so on, according to the Numeration Table (11).

Thus, in 123, the 1 is one hundred, the 2 is two tens, or twenty, the 3 is three units; and the whole number denoted is one hundred and twenty-three.

What would be the value of 4 in the first place on the right? In the second place? In the third place? In the fourth place?

Local Values of Figures.

(14.) The value of a figure is increased ten-fold for each place it is removed from units towards the left, in a row of figures this constitutes its local value.

In 25, 2 has the local value 2 tens, which is ten times the simple 2; in 125, 1 has the local value 1 hundred, which is ten times ten, the value that 1 would have in the second place.

The figure 3, in the second place from the right, would denote how many times the simple 3? In the third place from the right? In the fourth?

RULE I.

(15.) To numerate or read a row of Figures.

Call the successive figures units, tens, hundreds, &c., from right to left (11); and then read them, according to their respective values, from left to right.

Calling the figures, one after another, units, tens, hundreds, &c., from right to left, we find the last figure 7 to be tens of millions; then, reading from left to right, we say,

Seventy millions, three hundred and four thousand, five hundred and twenty-one.

RULE II.

(16.) To write in Figures any given Number..

Set proper figures, from left to right, to denote the descending orders of units, from the highest in the given number down to simple units-supplying each vacant place with a 0.

EXAMPLE.

To write in figures the number

Three millions, twenty-five thousand, and thirty. The descending orders of units in this number, are 3 millions, 2 tens of thous., 5 thousands, and 3 tens ; hence we write it thus:

30 250 30,

in which the vacant places of hundreds of thousands, hundreds, and units, are filled with Os.

EXERCISES.

Write in figures each of the following numbers:

1. One hundred.

14. Three thousand and five. 15. Eight thous. and nineteen. 16. Nine thous. and eleven. 17. Ten thousand.

18. Twelve thousand and ten. 19. Twenty thous. and nine.

2. Two hundred and one. 3. Three hundred and ten. 4. Four hundred and five. 5. Five hundred and fifteen. 6. Six hundred and twenty. 7. Seven hund. and thirty-four. 20. Four thousand and ninety. 8. Eight hundred and eleven. 21. Eleven thous. and eleven. 9. Nine hun. and ninety-nine. 22. Thirty thous. and sixteen. 10. One thousand. 23. Forty-one thous. & twelve. 24. Fifty thous. nine hundred. 25. Seventy-eight thous. & one.

11. Two thousand and nine. 12. Five thousand and ten.

13. Seven thous. one hundred. 26. Ninety thous. twenty-five.

27. One hundred thousand and 34. One million, two hundred and fifty-four thousand.

one hundred. 28. Two hundred and thirty 35. Two millions, forty thous., thous. and three hundred. six hundred and twenty.

29. Five hundred and one 36. Fifty millions, one hundred thous. two hund. and three.

30. Seven hund. and thirteen 37. thous. four hund. and fifty.

thousand, seven hundred.

Sixty-one millions, four hundred and ten thousand.

31. Nine hund. and ninety-nine 38. Two hun. and five millions, thous. and seventy-five.

32. Eight hund. and fifty-one 39. thous. one hund. and twen

ty-one.

four hundred and ninety-one

Four hundred and ten millions, six hundred and one thousand.

33. Seven hundred and eleven 40. Nine hundred millions, one thousand five hundred and thousand, eight hundred and nineteen. sixty-nine.

French and English Numeration.

(17.) In the French system of Numeration, which prevails in continental Europe and America, a thousand millions make one billion, a thousand billions make one trillion, &c.

In the English system, which was formerly used in this country, a million millions make one billion, a million billions make one trillion, &c.

This system, it is said, is now becoming obsolete in England. We sometimes find the higher numbers named in accordance with it, in scientific books, and it is necessary to notice the difference between the two systems.

In the French system, the number

3 840 930 670 820

is 3 trillions, 840 billions, 930 millions, 670 thousand, 820: In the English system, the same number would be called, 3 billions, 840930 millions, 670820.

CHAPTER II.

ADDITION.-SUBTRACTION.-MULTIPLICATION.-DIVISION.

ADDITION.

(18.) ADDITION consists in uniting two or more numbers in Thus 5 and 4 added together make 9; or the

one sum.

sum of 5 and 4 is 9.

What is the sum of 3 and 2?
What is the sum of 6 and 4?

What is the sum of 3 and 2 and 4?
What is the sum of 7 and 5 and 3?

The sum found may be regarded as a whole, of which the given numbers are the parts.

What is the sum of 4 and 6 and 8? Then what is the whole? and what are its parts? What is the sum of 10 and 6 and 4? Then what is the whole and what are its parts?

Commit to memory the elementary sums of numbers; thus 1 and 1 are 2, 1 and 2 are 3, &c.; 2 and 1 are 3, 2 and 2 are 4, &c., as given, from left to right, in the following

Addition Table.

1 and 1 are 22 are 33 are 44 are 55 are 66 are 77 are 88 are 99 are 10 2 and 1 are 32 are 43 are 54 are 65 are 76 are 87 are 98 are 109 are 11 3 and 1 are 42 are 53 are 64 are 75 are 86 are 97 are 108 are 119 are 12 4 and 1 are 52 are 63 are 74 are 85 are 96 are 107 are 118 are 129 are 13 5 and 1 are 62 are 73 are 84 are 95 are 106 are 117 are 128 are 139 are 14 6 and I are 72 are 83 are 94 are 105 are 116 are 127 are 138 are 149 are 15 7 and 1 are 82 are 93 are 104 are 115 are 126 are 137 are 148 are 159 are 16 8 and are 92 are 103 are 114 are 125 are 136 are 147 are 158 are 169 are 17 9 and 1 are 102 are 113 arc 124 are 135 are 146 are 157 are 168 are 179 are 18 10 and 1 are 112 are 123 are 134 are 145 are 156 are 167 are 178 are 189 are 19 11 and 1 are 122 are 133 are 144 are 155 are 166 are 177 are 188 are 199 are 20 12 and 1 are 132 are 14 3 are 154 are 165 are 176 are 187 are 198 are 209 are 21

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