DECIMAL FRACTIONS. 186. There are two kinds of Fractions in general use: CoMON FRACTIONS and DECIMAL FRACTIONS. A COMMON FRACTION is one whose unit is divided into any number of equal parts. A DECIMAL FRACTION is one whose unit is divided according to the scale of tens. 187. If the unit 1 be divided into 10 equal parts, each part is called one-tenth. If the unit 1 be divided into one hundred equal parts, or each tenth into ten equal parts, each part is called one-hundredth. If the unit 1 be divided into one thousand equal parts, or each hundredth into ten equal parts, the parts are called thousandths, and we have like expressions for the parts, when the unit is further divided according to the scale of tens. From which we see, that the fractional unit of a decimal is one of the equal parts arising from dividing the unit 1 accord ing to the scale of tens: hence, it is one-tenth, one-hundredth one-thousandth, &c. 188. A DECIMAL NUMBER, or decimal, is one which contains a decimal unit. 189. A MIXED DECIMAL, is one composed of a whole number and a decimal. Notation and Numeration. 190. The denominators of decimal fractions are seldom written. The fractions are expressed by means of a period, placed at the left of the numerator, called the decimal point (.) The denominator, however, of every decimal, is always understood : It is the unit 1, with as many ciphers annexed as there are places of figures in the decimal. The place next to the decimal point is called the place of tenths, and its unit is 1 tenth; the next place, at the right, is the place of hundredths, and its unit is 1 hundredth; the next is the place of thousandths, and its unit is 1 thousandth; and similarly for places still to the right. NOTE-Decimal fractions are numerated from left to right; thus, tenths, hundredths, thousandths, &c. They are read 4 tenths, 54 hundredths, 64 thousandths, &c. 1. That the denominator belonging to any decimal fraction is 1, with as many ciphers annexed as there are places of figures in the decimal. 2. That the unit of any place is ten times as great as the unit of the next place to the right-the same as in whole numbers: hence, whole numbers and decimals may be written together, by placing the decimal point between them. 186. How many kinds of fractions are there? What are they? What is a common fraction? What is a decimal fraction?-187. When the unit 1 is divided into 10 equal parts, what is each part called? What is each part called when it is divided into 100 equal parts ? When into 1000? Into 10,000? &c. How are decimal fraction formed?-188. What is a decimal number?-189. What is a mixed decimal?-190. Are the denominators of decimal fractions generally set down? How are the fractions expressed? Is the denominator understood? What is it? What is the place next the decimal point called? What is its unit? What is the next place called? What is its unit? What is the third place called? What is its unit: Which way are decimals numerated and read?—191. What are the two prin ciples of decimals ? 192. Rule for Writing Decimals. Write the decimal as if it were a whole number, prefixing as many ciphers as are necessary to make its right-hand fig ure of the required name. 193. Rule for Reading Decimals. Read the decimal as though it were a whole number adding the denomination indicated by the lowest decimal unit Write the following numbers in figures, and numerate them : 1. Twenty-seven, and four-tenths. 2. Thirty-six, and fifteen-thousandths. 3. Ninety-nine, and twenty-seven ten-thousandths. 4. Three hundred and twenty thousandths. 5. Two hundred, and three hundred and twenty millionths. 6. Three thousand six hundred ten-thousandths. 7. Five, and three-millionths. 8. Forty, and nine ten-millionths. 9. Forty-nine hundred ten-thousandths. 10. Fifty-nine, and sixty-seven ten-thousandths. 11. Four hundred and sixty-nine ten-thousandths. 12. Seventy-nine, and four hundred and fifteen millionths. 13. Sixty-seven, and two hundred and 27 ten-1000ths 14. One hundred and five, and ninety-five ten-millionths. 15. Forty, and 204 thousand millionths. 192. What is the rule for writing decimals?-193. What is the rule for reading decimals UNITED STATES MONEY. 194. The denominations of United States Money correspond to the decimal division, if we regard one dollar as the unit. For, the dimes are tenths of the dollar, the cents are hun dredths of the dollar, and the mills, being tenths of a cent, are thousandths of the dollar. Examples. 1. Express $37 and 26 cents and 5 mills, decimally. 3. Express $215 and 8 cents, decimally. 6. Express $15 6 cents 9 mills, decimally. ANNEXING AND PREFIXING CIPHERS. 195. ANNEXING a cipher is placing it on the right of a number. If a cipher is annexed to a decimal it makes one more de cimal place, and therefore, a cipher must also be added to the denominator (Art. 190). The numerator and denominator will therefore have been 194. If the denominations of Federal Money be expressed decimally what is the unit? What part of a dollar is 1 dime? What part of a lime is 1 cent? What part of a cent is a mill? What part of a dollar is 1 cent? 1 mill?-195. When is a cipher annexed to a nuinber? Does the annexing of ciphers to a decimal alter its value? Why not? What does five-tenths become by annexing a cipher? What by annexing two ciphers? Three ciphers? |