ORDER OF TENS. ART. 3. Nine units and one more are called Ten: it forms a unit of a second or higher order called Tens. Ten is represented by the same figure, 1, as a single thing, or unit of the first order; but, To distinguish ten, the 1 is written in the second order, the second place from the right hand: The first order, or right hand place, is filled with a cipher. The cipher, in the first place, denotes that there are no units of the first order. The number ten is written thus; 10 one more called? Ten forms When two figures are written a unit of what order? How is it written? together, what is the place on the right called? Ans. The first place, or first order, or unit's place. What the place on the left? Ans. The second place, or second order, or tens' place. 3. Ia writing ten, why is a naught put in unit's place? ten and one unit? How written? What are two tens? What are one How written? ART. 4. The numbers between 20 and 30, 30 and 40, &c., may be expressed by considering the tens and units of which they are composed. Thus, the number twenty-six is composed of two tens and 6 units; and is expressed by writing 2 in the place of tens, and 6 in the place of units, thus, . 26 Ninety-seven has 9 tens and 7 units; written, 97 ORDER OF HUNDREDS. ART. 5. Ten tens are One Hundred, which forms a unit of the third order called Hundreds. It is represented by the same figure, 1, as a single thing, or unit of the first order; but, The 1 is written in the third order, while the orders of tens and units arc each filled with a cipher, thus, 100. The mode of writing one unit, two units; one ten, two tens, &c., has been explained. In writing one hundred, two hundreds, &c., place the figure representing the hundreds in the third order, and fill the place of units and tens with ciphers, thus: Two hundred. . . . 200 Six hundred . . 600 ART. 6. With the three orders of UNITS, TENS, and HUNDREDS, all the numbers between one and one thousand may be expressed. In the number three hundred and sixty-five, are three hundreds, six tens or sixty, and 5 units; written, 365. The number four hundred and seven, contains 4 hundreds, 0 tens, and 7 units; written, 407. In the number seven hundred, are 7 units of the third order, and no units of the first and second orders, 700. REVIEW.-4. How are the numbers between 20 and 30, 30 and 40, written? 5. Of what order do ten tens form a unit? In writing one hundred, what orders are filled with ciphers? ORDER OF THOUSANDS. ART. 7. Ten hundreds, or ten units of the order of hundreds, are called One Thousand, which forms a unit of the fourth order. One thousand is expressed thus, Two thousand, thus, . Three thousand, thus, 1000 、 ART. 8. PRINCIPLES OF NOTATION AND NUMERATION. 1. Numbers are represented by the 9 digits and cipher. 2. The cipher or naught (0) has no value; it is used merely to fill vacant orders. 3. The number expressed by any figure depends upon the order or place which it occupies; Thus, 2 in the first order is 2 units; in the second order, 2 tons or twenty; in the third order, 2 hundreds, &c. 4. The number expressed by a figure standing alone, is called its simple value; the number expressed when combined with other figures, its local value. 5. The local value of a figure increases from right to left tenfold: ten units of the first order make one unit of the second; ten units of the second, one of the third. Invariably, ten units of any order make one unit of the next higher order. NOTE. When units are named, those of the first order are meant. ART. 9. The name of each of the first nine orders is learned from the Tuble of Orders. REVIEW.-6. With what three orders may the numbers between one and one thousand be cxpressed? In writing the number three hundred and five, what order would be filled with a cipher? Why? 7. Ten hundreds make a unit of what order? How expressed? In writing one thousand, what orders are filled with ciphers? Why? 8. By what characters are numbers represented? What value has the cipher? For what is it used? Upon what does the number expressed by a figure depend? What is 2 in the first place? In the second? In the third? What is the simple value of a figure? The local value? Iow does it increase? What is meant by tenfold? 9. Where learn the names of the first nine orders? Repeat the table. TABLE OF ORDERS. 9th. 8th. 7th. 6th. 5th. 4th. 3d. 2d. 1st. ART. 10. For convenience, the different orders are divided into periods, of three orders each. The first three orders, that is, Units, Tens, Hundreds, constitute the first or UNIT PERIOD. The second three orders, that is, Thousands, Tens of Thousands, Hundreds of Thousands, constitute the second. or THOUSAND PERIOD. The next three orders, that is, Millions, Tens of Millions, and Hundreds of Millions, constitute the third or MILLION PERIOD. ART. 11. Periods according to the Common Method: First period, Unit. Seventh period, Quintillion. For other methods of Numeration, see "Raj's Higher Arithmetic." REVIEW.-10. Why are the orders divided into periods? IIcw many rders constitute a period? What is the name of the first period. and of what orders is it composed? The name of the second period, and of what orders is it composed? The name of the third period? ART. 12. This Table shows the division into Periods. 5th Period. 4th Period. 3d Period. 2d Period. 1st Period. Trillions. Billions. Millions. Thousands. Units. ART. 13. The art of reading numbers when they are written in figures, is called NUMERATION. Rule for Numeration.-1. Begin at the right hand, and point off the numbers into periods of three figures each. Beginning at the left hand, read each period as if it stood alone; then add the name of the period. 10, ten; or one ten and no units. 25, twenty-five; or two tens and five units. 200, two hundred; or 2 hundreds, 0 tens, and 0 units. 305, three hundred and five; or 3 hundreds, 0 tens, and 5 units. 7405, seven thousand four hundred and five; or 7 thousands, 4 hundreds, 0 tens, and 5 units. 45068, forty-five thousand and sixty-eight; or 4 tens of thousands, 5 thousands, 0 hundreds, 6 tens, and 8 units. REVIEW.-12. Name the periods. 13. What is Numeration? Rule? |