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Thus, in the number 109,876,543,210,

the first

group is 210 ones,

the second group is 543 thousands,
the third group is 876 millions,

the fourth group is 109 billions.

17. Each complete group contains hundreds, tens, and ones of its group-name. Thus,

847,298,341, instead of being read 8 hundred-millions, 4 ten-millions, 7 millions, etc., is more briefly read, eight hundred forty-seven millions, two hundred ninety-eight thousands, three hundred forty-one.

EXERCISES.

60. In the number 321,654,987, what is the name of the first group? Of the third? Of the second?

61. Give the place name of the 1. Of the 2. Of the 3. Of the 5. Of the 9. Of the 6. Of the 4.

62. What figure expresses the 4th order of units? The 7th? The 5th? The 6th? The 8th ?

18. The method of writing numbers in figures is based on the following

Principles of Notation.

1. Ten units of any order equal one unit of the order next larger.

2. Each removal of a figure one place toward the left increases its value ten times, and each removal of a figure toward the right diminishes its value ten times.

19. Our system of Numbers is called a Decimal System, from the Latin decem, ten, because of the uniform ten-fold increase of units from any order to the next larger.

The successive orders of units in a number form a

Scale; and, where ten units of any order always make a unit of the next larger, the scale is ten or decimal.

20. A period (.), called the decimal point, may be written at the right of the ones' figure to mark the ones' place.

21. A number at the left of the decimal point is an Integer, or whole number, because it is a collection of entire ones.

22. Figures may be written at the right of ones, if separated from them by the decimal point.

23. The first figure at the right of ones is in the first decimal place, has the place-name tenths, and expresses the first order of decimal units, each being one tenth of a

one.

A figure at the right of tenths is in the second decimal place, has the place-name hundredths, and expresses the second order of decimal units, each being one tenth of a tenth.

A figure at the right of hundredths is in the third decimal place, has the place-name thousandths, and expresses the third order of decimal units, each being one tenth of a hundredth. Thus,

6.378 expresses six ones, and three tenths, seven hundredths, eight thousandths, or briefly six, and three hundred seventy-eight thousandths.

NOTE. In reading numbers use the conjunction and only after the ones to show the place of the decimal point.

24. A number at the right of the decimal point is a Decimal, or a collection of tenths, hundredths, thousandths, or other decimal parts of a one.

NOTE. In writing a decimal without an integer the ones' place may be filled with a zero. Thus,

Three hundred forty-one thousandths may be written 0.341.

25. The method of writing numbers, and the names of units, places, and groups are shown in the following

[blocks in formation]

ORDERS OF UNITS. 12th,11th, 10th, 9th, 8th, 7th, 6th, 5th, 4th, 3d, 2d, 1st, 1st, 2d, 3d.

[merged small][merged small][merged small][ocr errors]

3d,

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Ten-billions

Billions

Hundred-millions.

Ten-millions

Millions

[blocks in formation]

FIGURES.

GROUPS.

GROUP-NAMES.

2d,

1st,

1st Decimal, Thousandths.

4th,
Billions, Millions, Thousands, Ones,

The number in the table is, three hundred sixty-one billions, five hundred forty millions, seven hundred ninetythree thousands, one hundred fifty-four, and six hundred thirty-eight thousandths.

NOTE 1.-Group-names above billions are trillions, quadrillions, quintillions, etc.; below thousandths, millionths, billionths, etc.

NOTE 2. The left-hand group of the integer, or the right-hand group of the decimal may contain only one or two figures. The name of a partial decimal group is the same as the place-name of its right-hand figure. Thus, 16.84 is read sixteen and eighty-four hundredths.

EXERCISES IN WRITING NUMBERS.

63. Write in figures, thirty-five million six hundred twenty-seven thousand two hundred three, and sixteen hundredths.

35,627,203.16

Solution. Writing 35 for the millions, 627 for the thousands, 203 for the ones, and .16 for the hundredths, we have as the result required, 35,627,203.16.

64. Write in figures, three hundred twenty-nine thousand four hundred fifteen.

65. Write in figures, nine thousand seven hundred fiftytwo, and one hundred one thousandths.

26. Rule for writing Numbers.

Beginning at the left, write the figures of each group in their order, filling vacant places and groups with ciphers.

Write in figures:

66. Six thousand five hundred nine.

67. Eleven thousand nine hundred eleven.

68. Thirty-seven thousand four hundred eighty-nine. 69. Ninety thousand four hundred forty-four.

70. One hundred sixty-three thousand.

71. Two hundred twenty thousand two hundred sixty-two. 72. Five hundred seventy-four thousand three hundred thirty-five.

73. Seven hundred fifty-three thousand seven hundred fifty.

74. Five thousand four hundred eighty-nine.
75. Four hundred eighty thousand eight.
76. One million one hundred thirteen.

77. Three million three thousand thirty.

78. Nine hundred seven million eight hundred five thousand seventy-four.

79. Fifty-seven billion forty-four million ninety-three thousand eighty-three.

80. Thirteen million six hundred thousand one hundred seventy.

81. Five hundred six billion two million four thousand

one.

82. One thousand seven hundred sixty-two, and five tenths. 83. Nine hundred ninety-four, and thirty-eight hundredths.

84. One hundred nineteen thousand, and one hundred nineteen thousandths.

85. One million four hundred thousand three hundred, and thirty-three hundredths.

86. Sixteen thousand seven hundred forty-five, and eightysix thousandths.

87. Three billions three millions two thousands seven hundreds, and three thousandths.

EXERCISES IN READING NUMBERS.

88. Write and read 25362795.

25,362,795

Solution. 25362795 marked off into groups becomes 25,362,795. The first group from the right expresses 795 ones, or 795; the next group expresses 362 thousands; and the third expresses twenty-five millions. The whole is read: twenty-five million three hundred sixty-two thousand seven hundred ninety-five.

89. Write and read 3257893.

90. Write and read 64058.109.

64,058 109

be

Solution.-64058.109 marked off into groups comes 64,058.109, which is read sixty-four thousand fifty-eight, and one hundred nine thousandths.

91. Write and read 1673405.75.

92. Write and read 906005.805.

27. Rule for Reading Numbers.

Beginning at the ones' place, mark off the numbers by commas, into as many groups as possible of three figures each. Begin at the left and read each group as if it stood alone, giving the group-name except to the ones' group.

If there is a decimal, read it as if it were at the left of the point, and add the place-name of the last figure.

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