20. Numeration is a method of reading numbers represented by characters. 21. Notation is a method of writing, or representing numbers by characters. There are two methods of reading and writing numbers, viz.: the Arabic and the Roman. 22. In the Arabic Method numbers are expressed by means of ten characters. 23. The Arabic method of expressing numbers had its origin in India, but was introduced into Europe by the Arabs. 24. The Characters used in this system of expressing numbers are called figures. 4 567 9 25. The figures used and their names are as follows: Printed, 1 2 3 4 5 6 7 8 9 0 Written, 1 2 3 Named, One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Naught. 26. The first nine are called significant figures, because each always expresses a number. They are sometimes called digits, from the Latin digitus, a finger; it being once customary to count upon the fingers. 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. Thus, 10 means 1 ten 0 ones 11 12 1 "1 one ("endelfen," "2 ones ("twelif," 1 13 1 "3 66 14 1 "4 15 1 " 5 -one ten. and ten) eleven. -two and ten) twelve. ("thir and teen,"-three and ten) thirteen. ("four and teen,"-four and ten) fourteen. ("fif and teen," -five and ten) fifteen. 16, sixteen; 17, seventeen; 18, eighteen; 19, nineteen. 66 20 means 2 tens 0 ones ("tween ty," two tens) twenty. 1 one ("tween ty" and one,-two tens and one) 22, twenty-two. | 24, twenty-four. | 26, twenty-six. twenty-one. 28, twenty-eight. 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. The greatest number that can be represented by three figures is 999. Write in figures the following: 1. One hundred twenty-five. | 11. Seven hundred. 2. Four hundred fifty-nine. 3. Five hundred eighty. 4. Six hundred eleven. 12. Three hundred thirty. 13. Eight hundred one. 19. Seven hundred ten. 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. |