7. What is the greatest number expressed by one figure? Nine. 8. How is ten expressed? Ten is expressed by writing 1 in the second place, with a cipher on the right; as, 10. 9. What is the I called, standing in the second place? A unit of the second order. 1. Explain and write each of the numbers from ten to twenty. Eleven is composed of one ten and one unit, and is expressed by writing in the second place to denote the ten, and I in the first or right hand place to denote the unit; as, II. Twelve is composed of one ten and two units, and is expressed by writing 1 in the second place, and 2 in the first; as, 12. Thirteen is composed of one ten and three units, and is expressed by writing 1 in the second place, and 3 in the first; as, 13, etc. Twenty is two tens, and is expressed by placing 2 in the second place, and o in the first; as, 20. 2. Explain in like manner, and write each of the numbers from twenty to thirty. 3. From thirty to forty. 4. From fifty to sixty. so on to one hundred. From forty to fifty. From sixty to seventy; and 10. What is the greatest number that can be expressed by two figures? Ninety-nine. 11. How is a hundred expressed? A hundred is expressed by writing in the third place, with two ciphers on the right; as, 100. 12. What is the I called, standing in the third place? A unit of the third order. 5. Explain and write each of the numbers from one hundred to one hundred and ten. One hundred and one equals one hundred, no tens, 'and one unit, and is expressed by writing 1 in the third place, o in the second, and 1 in the first; as, 101. One hundred and two is expressed by 102; one hun dred and three by 103, etc. 6. Explain and write each number from one hundred and ten to one hundred and twenty. One hundred and ten is composed of one hundred, one ten, and no units, and is expressed by writing 1 in the third place, I in the second, and o in the first; as, 110. One hundred and eleven by 111; one hundred and twelve by 112, etc. 7. Explain in like manner, and write the numbers from one hundred and twenty to one hundred and thirty. 8. Write the numbers from one hundred and thirty to one hundred and fifty. From one hundred and fifty to two hundred. 9. Write two hundred. Three hundred. Four hundred. Five hundred. Write the following numbers in figures: 10. One hundred and twenty-three. II. Two hundred and thirty-seven. 12. Three hundred and forty-five. 13. Four hundred and ten. 13. What is the largest number that can be expressed by three figures? Nine hundred and ninety-nine. NOTE.-The preceding exercises should be repeated and supplemented by dictation, until the class become perfectly familiar with writing numbers less than a thousand. 14. How are numbers larger than 999 expressed? By Other Orders, called thousands, tens of thouBands, hundreds of thousands, millions, tens of millions, etc, each succeeding order having ten times the value of the preceding. 15. What is the general law by which the orders of units Increase? They increase from right to left by the scale of ten; that is, Ten simple units make one ten; Ten tens make one hundred; Ten hundreds make one thousand; and, universally, ten of any lower order make one of the next higher. 16. What places do the different orders occupy? Simple units occupy the right hand place; Tens, the second place; Hundreds, the third place; Thousands, the fourth place; Tens of thousands, the fifth place; Hundreds of thousands, the sixth place; Millions, the seventh place, etc.; the order of units corresponding with the place which the figure occupies.' 17. What is the effect of moving a figure from right to left, or from left to right. Its value is increased tenfold for every place it is moved from right to left; and is diminished tenfold for every place it is moved from left to right. 18. What are the different values of a figure called? The simple and local values. 19. What is the simple value of a figure? The simple value of a figure is the number of units it expresses when it stands alone. 20. The local value of a figure? Illustrate both. The local value is the number it expresses when connected with other figures, and is determined by the place it occupies, counting from the right. 21. What is the rule for expressing numbers by figures? Begin at the left hand, and write the figures of the given orders in their successive places toward the right. If any intermediate orders are omitted, supply their places with ciphers. Write the following numbers in figures: 20. One thousand, three hundred, and sixty. 21. Five thousand, seven hundred, and thirty-five. 22. Seven thousand, three hundred, and sixty-two. 23. Twenty-six thousand and seventy-five. 24. Thirty-seven thousand, one hundred, and six. 25. Ninety-five thousand and seventeen. 26. One hundred and twenty-three thousand and two hundred. 27. Three hundred and forty-eight thousand and two hundred. 28. Four hundred and ten thousand, three hundred, and forty. 29. Five hundred and forty thousand, six hundred, and thirty. 30. Six hundred thousand, two hundred and forty. 31. Seven hundred and fifty-five thousand, two hundred, and three. 32. Eight hundred and fifty thousand and three hundred. 33. Nine hundred and thirty-eight thousand and sixty-eight. 22. What is the Roman Notation; and why so called? The Roman Notation is the method of expressing numbers by letters; and is so called because it was employed by the Romans. 23. How many, and what letters are used? Seven capitals, viz.: I, V, X, L, C, D, and M. 24. What does each of these letters express? The letter I expresses one; V, five; X, ten; L, fifty; C, one hundred; D, five hundred; and M, one thou MDCCCLXXII, one thousand, eight hundred, and seventy-two. |