2. A Number is a unit or collection of units. 3. In counting a large number of objects it is natural to group them. Thus, coins are put in piles and the piles counted, envelopes in packages and the packages counted, etc. These piles and packages may themselves be piled and put in larger packages, and the process continued indefinitely. 4. To express numbers so that all may understand what is meant by the characters which represent them, the system of grouping by tens has been adopted. There are, therefore, single things, or units; groups of ten units, or tens; groups containing ten tens, or hundreds, etc. 5. The method of grouping by tens is called the Deci• mal System. Decimal is derived from the Latin word decem, which means ter. Numbers may be expressed by words or other characters, viz: figures and letters. 6. Notation is the method of expressing numbers by figures and letters. The Arabic Notation is the method of expressing numbers by means of figures. Its name is derived from the Arabs, by whom it was introduced into Europe. The Roman Notation is the method of expressing numbers by means of letters. It is so called because it was used by the ancient Romans. 7. Numeration is the method of reading numbers expressed by figures or letters. ARABIC SYSTEM. 8. In this system ten figures are employed to express numbers, viz: Figures. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 9. By combining these figures according to certain principles, we can express any number. 10. PRINCIPLE.-When figures are written side by side, the one at the right expresses units, the next tens, and the next hundreds. EXERCISES. 11. 1. In 79, what does the 7 express? What does the 9 express? Read the number, beginning at the left. 2. In 58, what does the 5 express? What does the 8 express? Read the number, beginning at the left. 3. In 740, what does the 7 express? What does the 4 express? What does the 0 express? Read the number. 4. Begin at the left and read 76, 176, 106, 360, 203. # 12. Figures in units' place express units of the first order; those in tens' place, units of the second order; those in hundreds' place, units of the third order, etc. 13. Numbers between 1 ten and 2 tens are named thus: 1 ten and 1 unit or 11, eleven. 1 ten and 2 units or 12, twelve.' 1 ten and 3 units or 13, thirteen. 1 ten and 4 units or 14, fourteen. 1 ten and 5 units or 15, fifteen. 1 ten and 6 units or 16, sixteen. 1 ten and 7 units or 17, seventeen. 1 ten and 8 units or 18, eighteen. 1 ten and 9 units or 19, nineteen. The words thirteen, fourteen, fifteen, etc., mean three and ten, four and ten, five and ten, etc. 14. The units of the second order are named as follows: The suffix ty means ten. Thus, forty means four tens, etc. The other numbers between 20 and 100 are read without the word and between the tens and units. twenty-seven, instead of twenty and seven. Thus, 27 is read |