Dictation exercises, both oral and written, should be given, until the pupil can write and read decimals with rapidity and correctness. Oral, thus, Ques., "The denominator of a fraction is 100, the numerator 7; what will express the decimal?" The prompt response should be, “Point, naught, seven, read, seven-hundredths" (.07). Ques. "The denominator is 1000, the numerator 35." Ans. “Point, naught, three, five, read thirty-five thousandths” (.035), etc. Also the converse; thus, Ques. “Point, naught, eight; what will express the fraction?" Ans. "The numerator is eight, the denominator one hundred, and the fraction is eight-hundredths" (180). Ques. "Point, naught, one, five?" Ans. "The numerator is fifteen, the denominator is one thousand, and the fraction fifteen-thousandths" (0), etc. 13. seer. 15. T. Express in the form of a decimal, 9. . 11. TOO 10. 1000 206 του σ 3027 10000 12.80. 14. 78880. 16. T. 262. Prefixing a cipher to a decimal multiplies the denominator by 10, and hence divides the decimal by 10 (200, 2). Thus, .5; .05 180; .005 = 1000; or, .5 10.05; .05 10.005, etc. = = = .7. 263. Rejecting a cipher from the left of a decimal divides the denominator by 10, and hence multiplies the decimal by 10 (200, 1). Thus, .007 To; .07=100;. .7 == ; or, .007 x 10.07; .07 × 10=. 264. Annexing a cipher to a decimal multiplies both numerator and denominator by 10, and hence reduces the fraction to higher terms (200, 3). Thus, .3 = † ; .30; 300=8% 1000 265. Rejecting a cipher from the right of a decimal divides both numerator and denominator by 10, and hence reduces to lower terms (200, 3). Thus, 18% = .600 ; f=.60;.6. 600 From the foregoing explanations are deduced the following 266. PRINCIPLES.—1. Decimals are governed by the same laws of notation as integers. Hence, 2. The value of any decimal figure depends upon the place it occupies at the right of the decimal sign. (258.) 3. Every removal of a decimal figure one place to the right diminishes its value tenfold. (262.) 4. Every removal of a decimal figure one place to the left increases its value tenfold. (263.) 5. Ciphers may be annexed or rejected at the right of any decimal, without changing its value. (264, 265.) 267. Express in figures and decimally; 1. Seventy-five thousandths. 1780.075. 2. Fifteen hundredths. 3. Seven thousandths. 6. 22 ten-thousandths. 7. 245 ten-thousandths. 4. Fifty-three thousandths. 8. 1042 hundred-thousandths. 5. Nine ten-thousandths. 10. 188. 10000 9. 14605 millionths 572 14. T. 08 16. 13067 100000 11.71% 13. 1271. 15. 841888. 17. 60000 RULE.-I. Write the numerator of the decimal as if an integer, writing ciphers in the place of vacant orders to give each significant figure its proper value, and place the decimal point before tenths. II. Read the decimal as if an integer, and give it the name of its right-hand order. In like manner express decimally the following fractions and mixed numbers: 18. 596 thousandths. 21. 74 millionths. 24. Four hundred thirty-seven thousand five hundred 49 millionths. 25. Three million forty thousand 12 ten-millionths. 26. Six hundred and 24 hundred-millionths. 27. Four hundred ninety-five million seven hundred five thousand and 43075 ten-millionths. 28. Four million seven hundred thirty-five thousand and 903624 hundred-millionths. DECIMAL CURRENCY. 268. Currency is coin, bank-bills, treasury notes, etc., employed in trade and commerce. 269. A Decimal Currency is a currency whose denominations increase and decrease by the decimal scale 270. The Legal Currency of the United States is a decimal currency; it is sometimes called Federal Money, because issued by the Federal Government. 271. Since the dollar is the unit of United States Money, dimes, cents, and mills are respectively tenths, hundredths, and thousandths of the unit. 272. Dollars should be written as integers, with the sign ($), prefixed; and dimes, cents, and mills, as decimals, with the decimal point at their left, or before tenths. Thus, 7 dollars 3 dimes 4 cents 5 mills, are written $7.345. 273. The denominations eagles and dimes are not regarded in business operations, eagles being tens of dollars, and dimes tens of cents. Thus, $34.27 is read 34 dollars 27 cents, instead of 3 eagles 4 dollars 2 dimes 7 cents. 274. Since the two places of dimes and cents, or of tenths and hundredths are appropriated to cents, when the number of cents is less than 10, write a cipher in the place of tenths. Thus, 9 cents are written $.09. (73.) 275. The half-cent may be written, either as a fraction (1), or as 5 mills. Thus, thirty-seven and a half cents are written $.37, or $.375. 276. Cents are often written as fractions of a dollar. Thus, $9.28 may be also written $9,28%. 277. In business transactions, if the mills in the final result are 5 or more than 5, they are considered a cent, if less than 5, they are not regarded. Thus, $5.197, would be called $5.20, and $5.194 would be called $5.19. 278. PRINCIPLES.-1. Decimal currency is expressed according to the decimal system of notation. 2. All the operations in Decimal Currency are the same as the corresponding operations in Decimals. REDUCTION OF DECIMALS. 279. To reduce decimals to units of lower or higher orders. ORAL EXERCISES. 1. How many tenths in 2 units? In 5 units? 2. How many tenths in 20 hundredths? In .40? 3. How many hundredths in 2 units? In 4 units? 4. How many hundredths in 200 thousandths? 5. How many hundredths in 5 tenths? In.6? .7? .8? 6. How many thousandths in .06 ? In .25? .48 ? .75? 7. How many hundredths in .150? In .260? In .2500? 8. In 400 thousandths how many hundredths? Tenths? 9. How many tenths of a dollar in $6? Hundredths? 10. Change 4 dollars 50 cents to cents. To mills. 11. How many dollars are 300 cents? 12. How many cents are 2600 mills? 540 cents ? Dollars? |