58. In numerating, or expressing numbers verbally, the various orders of units have the following names: 59. This method of numerating, or naming, groups the successive orders into periods of three figures each, there being three orders of thousands, three orders of millions, and so on in all higher orders. These periods are commonly separated by commas, as in the following table, which gives the names of the orders periods to the twenty-seventh place. and fifth fourth third ninth eighth seventh sixth first period. NOTE. This is the French method of numerating, and is the one in general use in this country. The English numerate by periods of six figures each. 60. The names of the periods are derived from the Latin numerals. The twenty-two given on the following page extend the numeration table to the sixty-sixth place or order, inclusive. 61. From this analysis of the principles of Notation and Numeracion, we derive the following rules: RULE FOR NOTATION. I. Beginning at the left hand, write the figures belonging to the highest period. II. Write the hundreds, tens, and units of each successive period in their order, placing a cipher wherever an order of units is omitted. RULE FOR NUMERATION. I. Separate the number into periods of three figures each, commencing at the right hand. II. Beginning at the left hand, read each period separately, and give the name to each period, except the last, or period of units. NOTE.-Omit and in reading the orders of units and periods of a number. EXAMPLES FOR PRACTICE. Write and read the following numbers: -: 1 One unit of the 3d order, two of the 2d, five of the 1st. Ans. 125; read, one hundred twenty-five. 2. Two units of the 5th order, four of the 4th, five of the 2d, six of the 1st. Ans. 24056; read, twenty-four thousand fifty-six. 3. Seven units of the 4th order, five of the 3d, three of the 2d, eight of the 1st. 4. Nine units of the 4th order, two of the 3d, four of the 1st. 5. Five units of the 4th order, eight of the 2d. 6. Five units of the 5th order, one of the 3d, eight of the 1st. 7. Three units of the 5th order, six of the 4th, four of the 3d, seven of the 1st. 8. Two units of the 6th order, four of the 5th, nine of the 4th, three of the 3d, five of the 1st. 9. Three units of the 8th order, five of the 7th, four of the 6th, three of the 5th, eight of the 4th, five of the 3d, eight of the 2d, seven of the 1st. 10. Three units of the 9th order, eight of the 7th, four of the 6th, six of the 5th, nine of the 1st. 11. Five units of the 12th order, three of the 11th, six of the 10th. 12. Four units of the 12th order, five of the 10th, eight of the 5th, nine of the 4th, four of the 3d. 13. Three units of the 15th order, six of the 14th, five of the 13th, three of the 9th, six of the 8th, five of the 7th, three of the 3d, six of the 2d, five of the 1st. 14. Five units of the 18th order, three of the 17th, six of the 16th, four of the 15th, seven of the 14th, eight of the 13th, four of the 12th, five of the 11th, six of the 10th, seven of the 9th, eight of the 8th, nine of the 7th, five of the 6th, six of the 5th, three of the 4th, two of the 3d, four of the 2d, eight of the 1st. 15. Two units of the 20th order, seven of the 19th, four of the 18th, eight of the 13th, five of the 6th, five of the 5th, five of the 4th, nine of the 1st. Write the following numbers in figures: 16. Forty-eight. 17. One hundred sixty-four. 18. Forty-eight thousand seven hundred eighty-nine. 19. Five hundred thirty-six million three hundred forty-seven thousand nine hundred seventy-two. 20. Ninety-nine billion thirty-seven thousand four. 21. Eight hundred sixty-four billion five hundred thirty-eight million two hundred seventeen thousand nine hundred fifty-three. 22. One hundred seventeen quadrillion two hundred thirty-five trillion one hundred four billion seven hundred fifty million sixtysix thousand ten. 23. Ninety-nine quintillion seven hundred forty-one trillion fifty-four billion one hundred eleven million one hundred one. 24. One hundred octillion one hundred septillion one hundred quintillion one hundred quadrillion one hundred trillion one hundred billion one hundred million one hundred thousand one hundred. 25. Four decillion seventy-five nonillion three octillion fiftytwo septillion one sextillion four hundred seventeen quintillion ten quadrillion twelve trillion fourteen billion three hundred sixty million twenty-two thousand five hundred nineteen. Write the following numbers in figures, and read them: 26. Twenty-five units in the 2d period, four hundred ninety-six in the 1st. Ans. 25,496. 27. Three hundred sixty-four units in the 3d period, seven hundred fifteen in the 2d, eight hundred thirty-two in the 1st. 28. Four hundred thirty-six units in the 4th period, twelve in the 3d, one hundred in the 2d, three hundred one in the 1st. 29. Eighty-one units in the 5th period, two hundred nineteen in the 4th, fifty-six in the 2d. 30. Nine hundred forty-five units in the 7th period, eighteen in the 5th, one hundred three in the 3d. 31. One unit in the 10th period, five hundred thirty-six in the 9th, two hundred forty-seven in the 8th, nine hundred twenty-four in the 7th. Point off and read the following numbers: ADDITION. 62. Addition is the process of uniting several numbers of the same kind into one equivalent number. 63. The Sum or Amount is the result obtained by the process of addition. 64. When the given numbers contain several orders of units, the method of addition is based upon the following principles: I. If the like orders of units be added separately, the sum of all the results must be equal to the entire sum of the given numbers. (Ax. 10). II. If the sum of the units of any order contain units of a higher order, these higher units must be combined with units of like order. Hence, III. The work must commence with the lowest unit, in order to combine the partial sums in a single expression, at one ope ration. 1. Find the sum of 397, 476, and 873. OPERATION 397 476 873 1746 ANALYSIS. We arrange the numbers so that units of like order shall stand in the same column. We then add the first, or right hand column, and find the sum to be 16 units, or 1 ten and 6 units; writing the 6 units under the column of units, we add the 1 ten to the column of tens, and find the sum to be 24 tens, or 2 hundreds and 4 tens; writing the 4 tens under the column of tens, we add the 2 hundreds to the column of hundreds, and find the sum to be 17 hundreds, or 1 thousand and 7 hundreds ; writing the 7 hundreds under the column of hundreds, and the 1 in thousands' place, we have the entire sum, 1746. 65. From these principles we deduce the following RULE. I. Write the numbers to be added so that all the units of the same order shall stand in the same column; that is, units under units, tens under tens, etc. II. Commencing at units, add each column separately, and write the sum underneath, if it be less than ten. |