Compound numbers reduced to Decimals of higher denom., . Decimal compound numbers reduced to whole numbers, ARITHMETIC. SECTION I. NOTATION AND NUMERATION. ART. 1. Any single thing, as a peach, a rose, a book, &c., is called a unit, or one; if another single thing is put with it, the collection is called two; if another still, it is called three; if another, four; if another, five, &c. The terms, one, two, three, four, five, &c., by which we designate how many single things or units are under consideration, are the names or expressions of numbers. Hence, 2. NUMBER signifies a unit, or a collection of units. OBS. Numbers have various properties and relations, and are applied to various computations and practical concerns of life. These properties and applications are formed into a system, called Arithmetic. Hence, 3. ARITHMETIC is the science of numbers. Numbers are usually denoted by certain letters of the alphabet; or by arbitrary characters called figures. QUEST.-1. What is a single thing called? If another is put with it, what is the collection called? If another, what? What are the terms one, two, three, &c.? 2. What does number signify? Obs. To what are numbers applied? 3. What is Arithmetic? How are numbers usually denoted? ΝΟΤΑΤΙΟΝ. 4. The art of expressing numbers by letters or figures, is called NOTATION. There are two methods of notation in use, the Roman and the Arabic. 5. The Roman method employs seven capital letters; viz : I, V, X, L, C, D, M. When standing alone, the letter I denotes one; V, five; X, ten; L, fifty; C, one hundred; D, five hundred; M, one thousand. To express the intervening numbers from one to a thousand, or any number larger than a thousand, we resort to repetitions and various combinations of these letters. The method of doing this will be easily learned from the following QUEST.-4. What is notation? How many methods are there in use? What are they? 5. What does the Roman method employ? What does each of these letters denote when standing alone? How are the intervening numbers from one to a thousand expressed? How denote Two? Four Six? Eight? Nine? Fourteen? Sixteen? Nineteen? Twentyfour? Twenty-eight? What does XL denote? LX? XC? CX? N.B. Questions on this table should be varied, and be continued by the teacher till the class becomes perfectly familiar with it. |