27. The figure 0, naught, is also called cipher and zero, and signifies no value or nothing, hence insignificant. 28. The Value of a figure is its power to express quantity. Figures have two kinds of value, viz.: Simple and Local. 29. The Simple value of a figure is the quantity which it expresses when it is alone. Thus 5 equals five, 8 equals eight. 30. The Local value of a figure is the quantity which it expresses by occupying a place in a number. Thus in 50, 5 equals fifty; in 800, 8 equals eight hundred. In the units' place of a number the simple and local values of a figure are the same. The terms used in expressing numbers by figures are places or orders, and periods. 31. The Place, or Order, of a figure is its position in a number. Thus in 365,5 is in the 1st Place; 6, in the 2d; and 3, in the 3d. 32. The name of the first place, or order is Units, or Ones. The greatest number of units expressed by one figure is 9. 33. The name of the second place or order is Tens. When two figures are used to express a number, the left-hand one expresses tens and the right-hand one ones. 10 means 1 ten 0 ones Thus, ten. 1 3 ("thir and teen," -three and ten) thirteen. 15 1 5 ("fif and teen," -five and ten) fifteen. 16, sixteen; 17, seventeen; 18, eighteen; 19, nineteen. 20 means 2 tens 0 ones (“tween ty," two tens) twenty. 21 ،، 2 1 one ("tween ty" and one, two tens and one) twenty-one. 28, twenty-eight. 22, twenty-two. 24, twenty-four. 26, twenty-six. 23, twenty-three. 25, twenty-five. 27, twenty-seven. 29, twenty-nine. The greatest number that can be expressed by two figures is 99. 34. The name of the third place or order is Hundreds. When three figures are used to express a number, the left-hand one expresses hundreds, the next, tens, and the next, ones. 100 means 1 hundred 0 tens 0 ones one hundred. one hundred one. one hundred ten. two hundred. The greatest number that can be represented by three figures is 999. Write in figures the following: 1. One hundred twenty-five. 2. Four hundred fifty-nine. 3. Five hundred eighty. 4. Six hundred eleven. 5. Eight hundred seventy. 10. Five hundred five. 11. Seven hundred. 12. Three hundred thirty. 13. Eight hundred one. 35. A Period consists of three places or orders. 36. In expressing numbers, the first three orders or places are regarded as forming a group, called the Period of Units. 37. The second group of three orders or places from the right is called the Period of Thousands. 123456 is composed of 123 thousands 456 units, or of two periods, and is read 123 thousand 456. 300004 is composed of 300 thousands 4 units, or of two periods, and is read 300 thousand 4. 4125 is composed of 4 thousands 125 units, or of two periods, and is read 4 thousand 125. 38. The third group of three orders or places from the right is called the Period of Millions. 451219149 is composed of 451 millions 219 thousands 149 units, or of three periods, and is read 451 million 219 thousand 149. 75000100 is composed of 75 millions 100 units, or of three periods, and is read 75 million 100. 3040000 is composed of 3 millions 40 thousand, or of three periods, and is read 3 million 40 thousand. 39. The fourth group of three orders or places from the right is called the Period of Billions. 412123000000 is composed of 412 billions 123 millions, or of four periods, and is read 412 billion 123 million. 90000050000 is composed of 90 billions 50 thousands, or of four periods, and is read 90 billion 50 thousand. 40. The names of the Orders of Units and the names of the Periods are given in the following SIXTH TABLE. FIFTH FOURTH THIRD SECOND FIRST PERIOD. PERIOD. PERIOD. PERIOD. PERIOD. PERIOD. Orders of Units. Number. 400 040 004 444 440 404 This number is read 400 quadrillion 40 trillion 4 billion 444 million 440 thousand 404. The Periods above Quadrillions are Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecil lions, Octodecillions, Novendecillions, Vigintillions, &c. PRINCIPLES OF NUMERATION AND NOTATION. 41. FIRST. Ten units of any order in a number are always equal to one unit of the next higher order. SECOND. Removing a figure one place to the left, increases its value tenfold. Removing a figure one place to the right, diminishes its value tenfold. THIRD. The name and value of the units represented by a figure in a number are always those of its order in that number. FOURTH. The absence of units in any order in anumber is denoted by a cipher. RULES FOR NUMERATION AND NOTATION. 42. NUMERATION. - Beginning at the right, separate the numbers into periods of three figures each. Then read the number in the first period at the left, adding the name of the period; do the same with each period in order toward the right, omitting to name the units period and any period or periods composed only of ciphers. NOTATION.-Beginning at the left, write the hundreds, tens, and ones of each period in their proper order, filling all vacant orders and periods with ciphers. 5. 142 205 10. 909 412 613 15. 425 003 16. 144 044 014 005 009 17. 75 000 000 000 075 18. 48 370 490 563 23. 19. 49 123 436 000 000 24. 20. 11 010 001 936 127 25. 21. 9 009 009 009 009 009 22. 41 000 041 000 041 000 3 000 000 000 000 000 62 410 000 443 000 413 125 679 456 199 |