4. The right-hand place is called the units' or ones' place. The next place to the left of the units is the tens' place. Note. We use the word unit for the word one, and units for ones. See Art. 12. If, as in 1 ten, 2 tens, etc., there are no ones or units to be expressed, we write the figure 0 in the units' place; thus, 10, 20. 5. The figure 0 does not express any number, but it is used to fill vacant places, as in the case above. It is called cipher or zero. It is a figure, but not a digit. 6. This is the decimal or tens' system of counting and of writing numbers. Note. For a simple illustration of this system, imagine a boy counting sticks. He counts ten and ties them together; then ten more, and so on till he has seven bundles and five sticks over. Then, writing 75, he shows that he has seventy-five sticks, the 7 being in tens, and the 5 in units' place. 7. Between twelve and twenty we call the ten "teen," which means "and ten"; as, fourteen, that is four and ten. From nineteen to ninety-nine we call the ten "ty," which means "times ten"; as, sixty, or six times ten; seventy-five, or seven times ten and five units. EXERCISES IN WRITING AND READING NUMBERS. Note.-Pupils should follow the forms of the digits given at the top of the preceding page, or other good copy. Let him here lay the foundation of neatness and accuracy in the writing and use of figures. 1. Write very neatly, in figures, the numbers from one to nine; from thirty to thirty-nine; forty to forty-nine; nineteen to ten; sixty to sixty-nine; ninety to ninety-nine; eighty-nine to seventy; fifty-nine to fifty; thirty-four to fifty-six. 2. Write in words: 75, 43, 51, 98, 29, 83, 11, 32, 64, 49, 17, 56, 19, 68, 31, 77, 99, 10, 24, 48. Note. The pupils may be required to show a number of jack-straws or of other objects equal to the numbers expressed. They should be arranged appropriately in tens and units. 3. How many tens are in twenty-eight? In sixty-two, fifty. six, ninety-five, eighty, seventy-one, forty-eight, sixty-five, thirtythree, fifty-one, etc.? 4. Write the following numbers in a column, and opposite each one express the same value in words: 92, 65, 38, 71, 40, 83, 14, 54, 17, 26, 90, 12, 83, 24, 75, 36. 5. The number 39 is expressed by two digits. What does the 9 stand for? The three? Which one, as it stands here, expresses the greater value? Why? 6. Answer the same questions in regard to 89, 48, 56, 35, 67, 22. Illustrate by objects. Note.-In English the digit expressing the tens is generally read first; as, forty-cight; but in the German language they say: eight and forty. Sometimes we hear the same in English. 7. Read the following numbers in the German way: 27 (seven and twenty), 36, 58, 67, 89, 38, 45. If the places of these digits were exchanged, would the numbers thus expressed be larger or smaller? Why? Illustrate by objects. 8. What is the greatest number that can be expressed by two figures? What is the smallest ? 9. Write in figures: Seventeen, thirteen, fifteen, twenty-eight, ninety-five, forty-two, eighty-three, thirty-four, sixty-nine, seventyseven, eighteen, fifty-one, sixty-seven, forty-eight, ninety-five, eighty-eight, thirty, sixty. 10. Read the following. (May be copied, or written at dictation, and then read.) 10, 19, 13, 18, 12, 17, 11, 16, 14, 20, 23, 21, 25, 27, 29, 22, 24, 26, 28, 32, 36, 31, 35, 33, 38, 37, 49, 44, 48, 41, 47, 50, 56, 52, 63, 75, 84, 95, 58, 67, 78, 89, 91, 65, 85, 96, 72, 15, 30, 35, 39, 42, 55. 11. The pupil may copy the following numbers: 56 34 67 23 11 89 78 45 98 10 87 54 32 43 21 65 76 17 26 49 61 88 39 58 72 99 30 27 83 57 Note.-Care should be taken that each number be recognized as a whole, that the pupil may not copy figures merely. He should recognize 56 as fifty-six, and not as the figures 5 and 6. 12. Take in at a glance as many numbers as you can, and repeat them, looking off the book: 16 78 23 62 43 50 84 31 58 46 55 13. The teacher may dictate two or more numbers at a time from exercises 10 and 11. 14. Write the number of jack-straws represented in each group below. The bundles are of ten each. # Suggestion.-Let the pupils make original notation exercises similar to the above, arranging the objects in groups, and noting the number both in words and figures. 8. Hundreds. If we count one more than ninety-nine we shall have nine tens and ten ones, or ten tens. Ten tens make one hundred. To express one hundred in figures we write 1 in the third place, thus, 100, filling the places of tens and units with ciphers. The 1 now stands for one hundred. A digit in the third place from the right stands for hundreds, and hence we write: 100 (one hundred), 200 (two hundred), 300 (three hundred), 400 (four hundred), 600 (six hundred), 700 (seven hundred), 800 (eight hundred), 900 (nine hundred). If with the hundreds we have to write any number of tens, as three hundreds and seven tens, we place the digit representing onek bere represented are woonet : read three hundred wrenty-fre We are learned is, that tea fua make rien, and ten tens make me hundred; 31. that in writing numbers the place on the right is the ones place; the be, the tens place; and the next, the hundreds place. EXERC SES N WRITING AND READ NG NUMBERS. 1 Express in gares: One hundred. six hundred, nine hundrei, seven hundred, four hundred, two hundred, etc. 2 Also, one hundred thirty, six hundred twenty, five hurdroi fighty, three hundred fifty, two hundred seventy, etc. 3. Also, one hundred sixty-five, three hundred eighty-four, Line handred seventy-one, four hundred thirty-three, etc. 4 How many hundreds in 481? How many tens? How many ones? How many of each in 385, 610, 974, 5:2, 137, 448? 5. Write the following numbers in a column, and opposite each the same number in words: 218, 117, 916, 675, 854, 370, 523, 388, 446, 770, 978, 101, 340, 620, 304. 100 6. Read, taking in at one glance as many numbers as possible: 102 909 808 910 Note-The foregoing numbers may be read in lines or columns, forward or backward, as the teacher may direct. 7. Write in figures the number of jack-straws represented in each of these groups. 8. Read 792. What does the 2 stand for? The 9? The ??-Show what each figure stands for in the following numbers : 439, 562, 101, 760, 875, 460, 140, 104, 583, 61. 9. In a number of three places, which figure is read first? Which represents the highest order? How would you write three hundred nine, having no tens? How would you write 7 hundred twenty, having no ones? Will it do to leave the place of the ones or tens vacant? Why? 10. What is the largest number that can be represented by three figures? What is the smallest whole number? 11. Write in figures: Three hundred fifty, six hundred eighty, two hundred seventy, eight hundred fifteen, four hundred twentyeight, nine hundred nine, one hundred ninety-six. 12. Copy the following, glancing at each number but once: (Think of the numbers represented, not merely of the figures to be written.) 107 400 212 560 801 118 180 215 419 711 999 103 205 340 409 583 655 728 846 979 893 13. Note.—The teacher may also dictate two or more of the foregoing numbers at once, thus quickening the attention of the pupils. 14. Write in regular order the numbers from 150 to 199; from 260 to 299; from 307 to 328; from 480 to 499; from 585 to 602; from 687 to 706; from 791 to 809. 15. Write in words the numbers from 337 to 345; also from |