132. Express in the form of a decimal, and read, Express in the form of a fraction, and read, 133. A mixed decimal consists of an inte decimal written together. In reading a mixed number, the word "and" is always re of the point. Thus, 7.12 is read, 7 and 12 hundredths; 26.134 and 134 thousandths. 134. The relation of integers and decimals to eac clearly shown in the following The number is read, 555 million 555 thousand 5 million 555 thousand 555 hundred-millionths or 2d. Hundreds. Tens. UNITS. Tenths. 4th. Thousandths. 5th. Ten-thousandths. 6th. Hund. -thousandths. 135. As in integers, so in decimals, make the order of units the starting-point of notation and numeration, extending the scale to the left of units' place in writing integers, and to the right of units' place in writing decimals. The first order to the left of units is tens, and the first order to the right of units is tenths; the second order at the left is hundreds, and the second order to the right is hundredths, and so on. The orders on the loft and the decimals on the right, equally distant from units' place, correspond in name, and are reciprocals of each other. Thus, the 2d order on the left is 1 ten, and the second order on the right is 1 tenth, and, or .1, is the reciprocal of 10; the 3d order on the left is 1 hundred, and the 3d order on the right is 1 hundredth, and, or .01, is the reciprocal of 100, etc. The value of any decimal order is always ten times the value of the next lower order, or 1 tenth the value of the next higher order. 136. In writing decimals, as in writing integers, vacant orders must be filled with ciphers. Since decimals are governed by the same laws of notation as integers, it follows that, 137. Each removal of a decimal figure one place to the right, causes it to represent units of one tenth the value it did before, and hence divides the number by 10. (17, III.) Thus, .03 is the value of .3; .003 is the value of .03; or, .3÷10 = .03; .03÷10 = .003. 138. Each removal of a decimal figure one place to the left, causes it to represent units of ten times the value it did before, and hence multiplies the number by 10. (17, II.) Thus, .05 is 10 times .005; .5 is 10 times .05; or, .05 × 10 = .5; 5. .005 × 10 = .05; 139. Ciphers annexed or rejected at the right of any deci WRITTEN 140. Express decimally : EXERCISES. 1. Seventy-five thousandths. 15.075. 2. Fifteen hundredths. 3. Seven thousandths. 6. 22 ten-thousandths. 7. 1. Fifty-three thousandths. 8. 5. Nine ten-thousandths. 10000 245 ten-thousandths. 9. 14605 millionths. 100000• 12. 3906 14. 572 15. 8418880 18. Four hundred thirty-seven thousand five hundred 49 millionths. 19. Three million forty thousand 12 ten-millionths. 20. Six hundred and 24 hundred-millionths. 21. Four hundred ninety-five million seven hundred five thousand and 43075 ten-millionths. 22. Four million seven hundred thirty-five thousand and 903624 hundred-millionths. 23. Three million forty thousand ten ten-millionths. 24. Twenty-four hundred-millionths. 25. Eight thousand six hundred forty-five hundred-thousandths. DECIMAL CURRENCY. 141. Currency is a term applied to all kinds of money in circulation, both coin and paper. The legal currency of the United States is a decimal currency, and is sometimes called Federal money. 1 DOLLAB 142. The unit of United States money are respectively tenths, hundredths, and thou- ERICA The legal coin of the United States is as follows: gold, the doubleeagle, eagle, half-eagle, quarter-eagle, three-dollar, and one-dollar pieces; silver, new currency-dollar, half-dollar, quarter-dollar, and ten-cent pieces; nickel, the five-cent and three-cent pieces; bronze, one-cent. The trade-dollar, used for commercial purposes, weighs 420 grains. The new currency-dollar of 1878 weighs 4121 grains. 143. In business transactions, cents are often written as fractions of a dollar; and the half-cent either as a fraction (1) or as 5 mills. Thus, $7.42 may be written, $742; 373 cents, $.371 or $375. Generally, in business calculations, if in the final result the mills are less than 5 they are not regarded; if 5 or more than 5, they are considered a cent. Thus, $6.424 would be called $6.42, and $6.426 would be called $6.43. This usage will generally be adopted in the answers to examples in this book. REDUCTION. 144. To change cents to mills, multiply by 10 cents, multiply by 100; dollars to mills, multip omitting the sign $, and writing cts., or m., after t Thus, $.36 36 cts.; $8 = 800 cts., or 8000 m. 145. To change mills to cents, divide by 10; lars, divide by 100; mills to dollars, divide by 100 fix the sign $ to the result. Thus, 740 mills = $.74, 645 cents = $6.45; 4200 mills = Since the dollar is the unit, of which cents are and mills are thousandths, it follows that 146. All the operations in DECIMAL CURREN same as the corresponding operations in DECIMALS 147. 1. How many tenths in 2 units? In 5 u 2. How many tenths in 20 hundredths? In .40 3. How many hundredths in 2 units? In 4 uni 4. How many hundredths in 200 thousandths? 5. How many hundredths in 5 tenths? In .6 ? 6. How many thousandths in .06? In .25? .4 7. How many hundredths in .150? In .260 ? 8. In 400 thousandths how many hundredths? 9. How many tenths of a dollar in $6? 10. Change 4 dollars 50 cents to cents. 11. How many dollars are 300 cents? 12. How many cents are 2600 mills? 13. How are thousandths changed to hundredt Hundr To mill 540 cents Dollars ? |