ARITHMETIC. SECTION I. NUMERATION AND NOTATION. 1. If we desire to know how many trees there are in a certain grove, we must count them; thus, one, two, three, four, five, six, seven, eight, nine, etc., until all have been counted. These expressions, one, two, three, etc., are called Whole Numbers, or Integers. 2. Notation is the method of representing numbers by means of characters. Numeration is the method of reading numbers when expressed by characters. ARABIC SYSTEM OF NOTATION. 3. Ten characters, called Figures, are used to represent numbers. They are 6, 7, FIGURES, 1, 2, 3, 4, 5, A figure standing alone expresses ones, or Units. 4. Numbers greater than nine are expressed by writing two or more of these figures side by side. If we add one more to nine, we shall have ten. To express this, we write 1 in the second place and zero in the first place. Hence A figure standing in the second place expresses Tens. Thus, 10 is ten units or 1 ten, called ten. And so on to 19, or nineteen. 20 is 2 tens, called twenty. 21 is 2 tens and 1 unit, or twenty-one. And so on to 29, or twenty-nine. In like manner we have 30, 40, 50, 60, 70, 80, 90, with the intervening numbers. EXERCISES. 1. Write neatly in figures the numbers from ten to twenty; from thirty to forty; from fifty to sixty; from seventy to eighty; from thirty-four to fifty-six; from sixty-six to eighty-six. How many tens and units in 2. 3. 4. 5. 14? 15? 25? 37? 26? 32? 39? 59? 35? 47? 54? 6. 40? 72? 60? 88? 7. 50? 79? 77? 8. 99? 80? 21? 9. What is the largest number that can be expressed by two figures? What is the smallest ? 5. Hundreds.-If we add one more to ninety-nine, we shall have ten tens, or one hundred. To express this, we write 1 in the third place. Hence A figure standing in the third place expresses Hundreds. Thus, 100 is 10 tens, called one hundred. 234 is 2 hundreds, 3 tens, and 4 units, or two hundred and thirty-four. 999 is 9 hundreds, 9 tens, and 9 units, or nine hundred and ninety-nine. EXERCISES. 1. Write neatly in figures the numbers from one hundred to one hundred and twenty-five; from two hundred and twentyfive to two hundred and fifty; from three hundred and fifty to three hundred and seventy-five; from four hundred and seventy-five to five hundred. If we add one more to nine, we shall have ten. To express this, we write 1 in the second place and zero in the first place. Hence A figure standing in the second place expresses Tens. Thus, 10 is ten units or 1 ten, called ten. And so on to 19, or nineteen. 20 is 2 tens, called twenty. 21 is 2 tens and 1 unit, or twenty-one. And so on to 29, or twenty-nine. In like manner we have 30, 40, 50, 60, 70, 80, 90, with the intervening numbers. EXERCISES. 1. Write neatly in figures the numbers from ten to twenty; from thirty to forty; from fifty to sixty; from seventy to eighty; from thirty-four to fifty-six; from sixty-six to eighty-six. How many tens and units in 2. 14? 26? 35? 47? 3. 4. 15? 25? 32? 39? 54? 5. 6. 37? 40? 59? 72? 60? 88? 7. 50? 79? 77? 8. 99? 80? 21? 9. What is the largest number that can be expressed by two figures? What is the smallest? |