THIRD BOOK WHOLE NUMBERS NOTATION AND NUMERATION Definitions 1. Quantity is anything that can be measured; as, weight, length, value, time. 2. A unit is any standard of reference employed in counting a collection or in measuring a quantity; as, a pound, a yard, a dollar, a day. 3. A number is the direct answer to the question: How many? 4. One is the simplest number and is called the unit of number, or unity. 5. The first nine numbers, sometimes called the simple numbers, are: one, two, three, four, five, six, seven, eight, nine. 6. An amount is an expression denoting the number and kind of units in a quantity; as, two pounds, five yards, six dollars, five head. 7. Similar amounts are such amounts as are composed of the same kind of units; as, three bushels and five bushels. 1 8. Numeration is the method of expressing numbers in words. 9. Notation is the method of expressing numbers by means of characters called numerals. 10. The Arabic notation, the system in general use, is so named because it was introduced into Europe by the Arabs. 11. The Roman system of notation, which is employed only for special purposes, is so named because it was the system in use among the ancient Romans. Arabic System 12. The Arabic numerals, called figures, used to express numbers, are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; named, naught, one, two, three, four, five, six, seven, eight, nine. 13. The figure 0 is also called cipher or zero; the figures 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits. When ten is thought of called a ten. Two tens 14. Nine and one make ten. as a single group, the group is make twenty; three tens, thirty; four tens, forty; and so on to ninety. The tens are expressed in figures by writing O after each of the nine digits in turn; as, 10, 20, etc. 15. If each of the first nine numbers is united in turn with ten, the numbers eleven, twelve, thirteen, fourteen . to nineteen are formed; if united with twenty, the numbers twenty-one, twenty-two... to twenty-nine are formed; and so on until ninety-one, ninety-two . . . to ninety-nine are formed. 16. A number consisting of tens and units is expressed by two figures, the right-hand figure expressing the number of units, and the left-hand figure, the number of tens. 17. Ten tens make one hundred. One hundred thought of as a single group is called a hundred. Hundreds, like units and tens, are numbered from one to nine inclusive, forming the numbers one hundred, two hundred, three hundred, and so on to nine hundred. The hundreds are expressed in figures by writing 00 after each of the nine digits in turn; as, 100, 200, etc. 18. If each number less than one hundred is united in turn with one hundred, the numbers one hundred one, one hundred two . . . to one hundred ninety-nine are formed; if united with two hundred, the numbers two hundred one, two hundred two . . . to two hundred ninety-nine are formed; and so on, until the numbers nine hundred one, nine hundred two . . . to nine hundred ninety-nine are formed. 19. A number consisting of hundreds, tens, and units is expressed by three figures: the first, counting from the right, expresses the number of units; the second, the number of tens; and the third, the number of hundreds. When there are no tens, a cipher is written in tens' place; when no units, a cipher is written in units' place. Thus, 268 expresses two hundred sixty-eight; 307, three hundred seven; 240, two hundred forty. 20. Units, tens, and hundreds are called, respectively, units of the first, second, and third order. |