COMPLETE PRACTICAL ARITHMETIC. NOTATION AND NUMERATION. 1. A Unit is one, or one thing; as one, one orange, one dollar. 2. A Number is that which tells how many, and consists of one or more units. 3. The Unit of a Numper is one of its units. The unit of seven men is one man. The unit of seven is one. 4. Numbers having the same unit are Like Numbers. Thus, 3, 4, and 5; 6 apples, 4 apples, and 3 apples; are like numbers. 5. A number not applied to any particular object is an Abstract Number; as 6, 11, 15. 6. A number that is applied to any particular object is a Concrete Number; as 6 men, 11 pounds, 15 days. 7. An Integer is a whole number. 8. The expression of numbers by figures or letters is called Notation. 9. The expression of numbers by figures is called Arabic Notation. It was used by the Arabs. 10. The expression of numbers by letters is called Roman Notation. It was first used by the ancient Romans. 11. The reading of numbers is called Numeration. 12. Figures are the characters used to express numbers. ARABIC NOTATION. In the Arabic notation ten different figures are used; they are: O, 1, 2, 3, 4, 5, 6, 7, 8, 9. Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. NOTE. - Naught is sometimes called zero, and cipher. The other nine figures are called digits, from a Latin word meaning fingers. 13. Naught used alone expresses no units, or nothing. The other nine figures express the number of units indicated by their names. 14. To express a number larger than nine, two or more figures are written side by side. 15. A figure standing alone expresses one or more units. 16. When figures stand side by side, the right-hand figure expresses units, the next tens, the next hundreds, etc. 17. The value of a figure, without regard to its place, is its Simple Value. The value of a figure with reference to its place in a number is its Local Value. NOTE. In the number 5555, the simple value of each figure is 5. The local value of the right-hand figure is 5. Of the second, 50. Of the third, 500. Of the fourth, 5000. 18. Figures in the units' place express units of the first order; those in the tens' place express units of the second order; those in the hundreds' place, units of the third order; etc. 19. The units of the second order, or tens, are ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety. One ten is written 10; two tens, 20; three tens, 30; etc. 20. The numbers between 10 and 20 are one ten and one unit, or 11; one ten and two units, or 12; one ten and three units, or 13; one ten and four units, or 14; etc. 21. Two tens and one unit is 21; five tens and six units is 56; nine tens and four units is 94; etc. 22. Write all the numbers between nine and twenty; between twenty and forty. 23. Write all the numbers between sixty and ninety. 24. Write four units of the second order and six units of the first order. 25. What number is expressed by writing seven units of the second order and five units of the first order? 22. Numbers having three figures are written with the hundreds at the left of the tens. Figures in the third place are called units of the third order. Thus, 482 is read four hundred eighty-two. 40. Five hundreds, eight tens, six units. 41. 9 hundreds, 5 tens, 3 units. 42. 7 hundreds, 0 tens, 0 units. 43. 4 hundreds, 0 tens, 6 units. 44. Nine hundred ninety. 45. Nine hundreds, nine tens, 9 units. 46. 8 units of the third order, 6 units of the second order, 2 units of the first order. 47. Five units of the 3d order, 6 units of the 1st order. 23. Units of the fourth order are written at the left of hundreds' place. Thus, 4876 is read four thousand eight hundred seventysix, or 4 thousands, 8 hundreds, 7 tens, 6 units. 57. Two thousand nine hundred twenty-six. 58. 5 thousands, 6 hundreds, 4 tens, 8 units. 59. 6 thousands, 0 hundreds, 0 tens, 2 units. 60. Six thousand four hundred eight. 61. Six thousand eight. 62. Six thousand eighty. 63. 5 units, 5 tens, 5 hundreds, 5 thousands. 24. On the same principle units of the fifth order occupy the fifth place, and are called ten-thousands. Units of the sixth order occupy the sixth place, and are called hundredthousands. Units of the seventh order occupy the seventh place, and are called millions. 25. Ten units of any order make one unit of the next higher order. 26. The first ten orders of units are shown in the following TABLE. 10th 9th 8th 7th 6th 5th 4th 3d 2d 1st 27. For convenience in reading and writing numbers they are separated into groups of three figures each, called periods. Each group takes the name of its right hand order of units; thus, the first group is the group of units, the second of thousands, the third of millions, the fourth of billions. The comma is used to separate the groups. Thus, in the number 624,503,275,320, the first group is 320 units, The above number is read as follows: NOTE. 624 billion, 503 million, 275 thousand, 320. In reading numbers the last group-name is always omitted |