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12. The first nine numbers are each expressed by a single figure, and are called units of the first order.
13. Since there is no single character to express the number ten, by grouping ten ones or units of the first order into a larger collection, there is formed a unit of the second order, called ten, written 10.
In the same manner are expressed,
6 hundred, by 600.
8 hundred, by 800.
The numbers from one hundred to nine hundred ninetynine inclusive are expressed by writing hundreds in the third place from the right, tens in the second place, and units in the first place.
The greatest number that can be expressed by three figures is 999.
The numbers from one thousand to nine thousand nine hundred ninety-nine are expressed by writing thousands in the fourth place from the right, hundreds in the third place, tens in the second place, and units in the first place.
The greatest number that can be expressed by four figures is 9999.
16. In the same manner, other new orders are formed to represent larger numbers, by grouping ten units of the fourth order to form the fifth order, or tens of thousands; and ten units of the fifth order to form the sixth order, or hundreds of thousands, etc.
10 Units (1)
10 Tens (10)
Thus, 432076 represents 6 units of the first order, 7 units of the second order, 0 units of the third order, 2 units of the fourth order, 3 units of the fifth order, and 4 units of the sixth order, and is read, Four hundred thirty-two thousand seventy-six.
make 1 Ten,
7 thousand, by 7000.
8 thousand, by 8000.
17. Orders of units are denoted by the position of the figures used in expressing a number.
Thus, 532 represents 2 units of the first order, 3 units of the second order, or 3 tens, and 5 units of the third order or 5 hundreds, and is read five hundred thirty-two.
PRINCIPLES.-I. Ten units of any order in a number make one unit of the next higher order.
II. When a figure is moved one place to the left, it represents units of ten times the value it did before.
III. When a figure is moved one place to the right, it represents units of one tenth the value it did before.
When any order of units in a number is vacant, the place should be filled with a cipher.
18. Copy and read the following numbers, naming in each the number of units of each order:
Write in figures and read:
1. Seven units of the fourth order, eight of the second order, and three of the first.
2. Three units of the fifth order, two of the third, and one of the first.
3. Two units of the sixth order, nine of the fifth, four of the third, one of the second, and seven of the first.
4. Forty-seven thousand six hundred forty.
5. One hundred forty-six thousand five hundred. 6. Ninety-five thousand three hundred ten.
7. Four hundred seventy thousand two hundred.
19. A period is a group of three orders of units, counting from right to left.
The first period on the right is called UNITS' PERIOD, the second, THOUSANDS' PERIOD, the third, MILLIONS' PERIOD, etc., as shown in the following
Beginning at the right, the order of simple units occupies the first place; tens, the second place; hundreds, the third; thousands, the fourth; tens of thousands, the fifth; hundreds of thousands, the sixth; millions, the seventh, etc.
Each period is read like a number of three figures, giving it the name of the period; thus, the first number above is read, 504 billion 127 million 364 thousand 549.
20. RULE FOR NOTATION.—Begin at the left, and write the hundreds, tens, and units of each period in their proper order, filling all vacant orders and periods with ciphers.
21. RULE FOR NUMERATION.-1. Begin at the right, and separate the number into periods of three figures each.
2. Begin at the left, and read each period as if it were units, giving each its name.
22. Express the following numbers by figures:
1. Twenty-six thousand twenty-six.
4. Four hundred fifty thousand thirty-nine.
5. Seven hundred twenty thousand fifty-six.
6. Two hundred forty-nine thousand five hundred.
7. One million ninety-six thousand two hundred ten.
8. Seven million thirty-six.
9. Five hundred sixty-three thousand four.
10. One million ninety-six thousand.
11. Ten million ten thousand ten hundred ten.
12. Four hundred eighty-three million eight hundred sixteen thousand one hundred forty-nine.
13. Seven hundred fifty million six thousand nine hundred. 14. Ninety-nine billion thirty-seven thousand four.
15. Five billion eighty million one hundred ten thousand seventy-five.
16. Ten million two hundred forty thousand seventeen. 17. Four hundred twenty-six billion twelve million eight hundred sixty.
18. Four hundred eighty-three million eight hundred sixteen thousand one hundred forty-nine.
Copy, point off, and read the following numbers:
22. 600317. 23. 108300. 24. 100103.
35. 3730016000. 36. 42020871400.