NOTE. The zero is often called an insignificant figure, and the other nine digits significant figures; but there is no foundation for the distinction. The zero performs an office precisely similar to that of any other figure, as the above explanation of the use of the figures used in writing 2503 clearly shows. Even when standing by itself it is as expressive as any other figure. (f.) The decimal point is often omitted in writing numbers; but in all such cases it is understood to belong at the right of the given number, thus making the right hand figure represent units. 9. Method of reading Numbers. In reading numbers expressed by figures we begin at the left hand, i. e., with the highest denomination. (a.) 546 = five hundreds, four tens, and six units, and is read five hundred and forty-six. (b.) 398 three hundreds, nine tens, and eight units, and is read three hundred and ninety-eight. (c.) 407: = four hundreds, no tens, and seven units, and is read four hundred and seven. (d.) 180 one hundred, eight tens, and no units, and is read one hundred and eighty. (e.) 64 or 064 = six tens and four units, and is read sixty-four. 10. Exercises in reading and writing Numbers. Read the following numbers, and also give the value of each in hundreds, tens, and units: 10. Explain the use of each figure used in the above numbers, as in the following model: — MODEL. In the first number, 507, the 7 marks the units' place, and shows that there are 7 units; the 0 marks the tens' place, and shows that there are o tens; the 5 marks the hundreds' place, and shows that there are 5 hundreds. 11. How will you write four hundred and seven ? Ans. By writing 4 in the hundreds' place, 0 in the tens', and 7 in the units'; thus, 407. 12. How will you write two hundred and seventeen? 13. How will you write eight hundred and forty-one? 14. How will you write eight hundred and twelve? 15. How will you write seven hundred and forty-six? 16. How will you write six hundred and ninety-four? 17. How will you write nine hundred and sixty-four? 18. How will you write four hundred and sixty-nine? 19. How will you write nine hundred? 20. How will you write seven hundred and eighty? 11. Number of Decimal Places unlimited. Extending these principles, we can take as many places as we please, by giving to the figure in each ten times the value it would have if written one place farther to the right. The names of the places as far as the twenty-fourth are given in the following example. 12. Division into Periods. (a.) By inspecting the above example it will be seen that the -- first three places are occupied by units, tens, and hundreds, the second three by thousands, tens of thousands, and hundreds of thousands, the third three by millions, tens of millions, and hundreds of millions, and so on. If the first three places were called, as they might be with perfect propriety, units, tens of units, and hundreds of units, and we should divide the number into periods of three figures each by commas, the first period would be the period of units, the second the period of thousands, the third of millions, the fourth of billions, &c. (b.) The right hand figure in each period expresses units or ones of the denomination of that period, while the second figure expresses tens, and the third, or left hand figure, expresses hundreds of that denomination. (c.) This is exhibited in the following table: 24th, or hundred-sextillions' place,.. 15th, or hundred-trillions' place,.... 12th, or hundred-billions' place,.... 9th, or hundred-millions' place, .... ..... 6th, or hundred-thousands' place,.. 3d, or hundreds place, 000,000,000,000,000,000,000, 000 13. Exercises to secure Familiarity with the Places and Periods. 1. What is the name of the first period at the left of the point? of the second period? of the third? of the fourth? of the fifth? of the sixth? of the seventh? of the eighth? 2. What is the name of the period occupying the first, second, and third places at the left of the point? 3. Occupying the fourth, fifth, and sixth places? 4. Occupying the seventh, eighth, and ninth? 5. Occupying the tenth, eleventh, and twelfth? 6. Occupying the thirteenth, fourteenth, and fifteenth? 7. Occupying the sixteenth, seventeenth, and eighteenth? 8. Occupying the nineteenth, twentieth, and twenty-first? 9. Occupying the twenty-second, twenty-third, and twenty fourth? 10. What is the number of the millions' period? Ans. The third period at the left of the point. 11. What is the number of the thousands' period? 21. Quadrillions' period? 22. Thousands' period? 26. In which place of what period would the fourth figure at the left of the point be? Ans. In the first place of the second or thousands' period. 27. In which place of what period would the seventh figure at the left of the point be? 28. Would the tenth ? 48. What would be the of the above-named places? 38. Would the thirteenth ? denomination of a figure in each Ans. The denomination of a figure in the fourth place at the left of the point would be thousands, that of a figure in the seventh place at the left would be millions, that of the tenth would be billions, &c. 49. Where must a figure be placed to represent trillions? Ans In the first place of the fifth period, which is the thirteenth place. at the left of the point. (a.) In reading a number represented by figures, we ordinarily commence at the left hand, and read each period as though its figures stood alone, giving afterwards the name of the period. For instance, the number 42,000,070,294,600,706 would be read in the same way. and would express, the same value, as if written 42 quadrillions, 70 billions, 294 millions, 600 thousands, and 706. NOTE. The scholar should regard a mistake in reading numbers as one of the most dangerous which can be made, for he will not only be likely to copy the numbers in the same manner as he reads them, but he will give those to whom he reads a false idea, which, unless they have the figures before them, they cannot correct. (b.) Read each of the following numbers: 1. 43,271. 2. 500,207. 3. 24,000,217. 4. 53,279,412. 19. 53,729,415. 20. 21,437,986,512. 21. 42,000,042,042. 22. 547,547,547,547. 23. 101,101,101,101. 24. 2,002,002,002,002. 25. 130,201,040,999,999. 26. 73,006,200,474. 2,008,002,008,002,008. 27. 900,000,726,000. 150,437,986,216. 9. 20,020,020,020. 10. 200,200,200,200. 11. 12. 70,000,007,700,077. (c.) Explain the use of the figures used in writing the above numbers. (See model following the 10th example in 10.) |