In Articles 101, 102, and 114 the division of decimals by integers has been taught. These the pupil may review. To divide an Integer or a Decimal by a Decimal. WRITTEN WORK. 293. ILLUSTRATIVE EXAMPLE I. Divide 72 by 1.2 Explanation. — Before dividing by a fraction, the dividend must be expressed in the same denomina1.2) 72.0 tion as the divisor. The divisor is a number of 60 tenths; the dividend expressed in tenths is 72.0 (720 tenths). 720 tenths divided by 12 tenths gives the same quotient as 720 divided by 12, which is 60. Ans. 60. WRITTEN WORK. 294. ILLUSTRATIVE EXAMPLE II. Divide 1.935 by 0.45 Explanation. Here the divisor is a num ber of hundredths ; the dividend expressed as 0.45) 1.93 5 (4.3 hundredths is 193.5 hundredths (the denomi180 nation may be indicated in the written work 135 by a caret). 135 193.5 hundredths divided by 45 hundredths gives the same quotient as 193.5 divided by 45, which is 4.3. Ans. 4.3. 295. From the preceding examples may be derived the following Rule. 1. To divide by decimals : Express the dividend in the came denomination as the divisor by putting a mark as many places to the right of the decimal point as there are decimal places in the divisor. 2. Divide as if the divisor were an integer, making a decimal point in the quotient, when the terms of the dividend have been used as far as the mark. NOTE. When there is a remainder after all the terms of the dividend have been used, the division may be continued, as in Articles 102 and 106. 296. Examples for the Slate. 107. How many books at $ 0.08 each can be bought for $ 3.84 ? 108. At $ 2.80 per yard, how many yards of muslin can be bought for $55.30 ? 109. How many rods, each 16.5 feet, are there in 99 feet? 110. One quart dry measure equals 67.2 cubic inches; one quart liquid measure equals 57.75 cubic inches : in a keg whose capacity is 5040 cubic inches, how many quarts dry measure ? How many quarts liquid measure ? 111. If coal is $6.67 per ton, how much coal can be bought for $ 3.335 ? 112. At $ 0.125 per yard for cotton cloth, how many yards can be bought for $ 25 ? Divide Divide (113.) 14.91 by 7. (126.) 56.28 by 0.0056 (114.) 8.25 by 1.5 (127.) 0.417196 by 58.76 (115.) 3.24 by 0.81 (128.) 0.08 by 1.611 (116.) 0.00468 by 0.013 (129.) 1.3 by 197.59 (117.) 180.375 by 1.625 (130.) 1203.488 by 28.6 (118.) 579 by 0.07 (131.) 49.2654756 by 0.0759 (119.) 6.9705 by 0.45 (132.) 2464.176 by 57.2 (120.) 0.0033 by 0.011 (133.) 164.6156 by 1334. (121.) 0.705 by 7.5 (134.) 0.789 by 0.037 (122.) 3 by 29.9 NOTE. First multiply both divi. (123.) 20 by 0.013 dend and divisor by 7. (124.) 4066.2 by 0.648 (135.) 1.36 by 5.807 (125.) 68077 by 71.66 (136.) 43.2} by 0.58} 137. Multiply 0.648 by 100; divide the product by lo; divide this quotient by 0.001; and multiply the result by } of 0.0362. 138. Find the sum of the following: 756.02 x to; 18.3 x 100; 0.7 -0.001; 8.16 - 187; and 0.24 - 16. For other examples in division of decimals, see page 135. 297. DRILL TABLE NO. 6. Decimals. E F G Ex. amples. 1. 5000. 2 1.648 3. 0.657 4. 0.002 0.025 Twenty-five, and two thousandths. 5. 0.005 6. 448. 7. 2.5 10. 0.708 Two, and twenty-five hundredths. 607. 11. 19.364 Seven hundred one, and six tenths. 18.08 12. 0.0516 Two, and 206 thousandths. 9.16 13. 1.732 936 ten-thousandths. 800.1 14. 8016. 54, and 54 thousandths. 0.0052 15. and 1047 millionths. 2.0763 16. 0.012 5 hundred, and 26 hundredths. 18.26 17. 12.007 One thousand millionths. 0.0101 18. 45.9 Twenty-nine millionths. 3.0712 19. 8.621 846291 hundred-thousandths. 80.06 20. 10.00562 Five hundred eleven thousandths. 5.4 21. 1002. 4271, and 4271 ten-millionths. 0.6805 22. 1.871 68 thousand, and 4tenths. 4.071 23. 0.121 One hundred twenty-two thousandths. 24.40 24. 1.015 Eight, and 47 hundredths. 0.0002 25. 8.33 Five hundred, and ; tenths. 1.071 298. Exercises upon the Table. 177. Read the numbers expressed in E.* 192. Divide E by F. 193. Divide G by E. 191. Multiply F by G. 194. Divide G by F. 195. Multiply E by 10 ; divide F by 100 ; add the results to G. What are DECIMAL FRACTIONS ? How are their written expressions distinguished from those of integral numbers ? What indicates the denomination of the decimal ? How do you read a decimal expression ? Read 7.05 as a mixed number; as a fraction. Read 0.504 and 500.004 so that they may be distinguished. How do you write decimals? What is the effect of annexing ciphers to a decimal expression ? How do you change decimals to common fractions ? Common fractions to decimals ? What fractions cannot be changed wholly to a decimal form ? What are they called when expressed decimally? How do you change a circulate to a common fraction ? How do you add and subtract decimals ? Perform an example in multiplication by a decimal, explain and give the rule. Perform an example in division by a decimal, explain and give the rule. How do you express the multiplication of a decimal by 10; 100; 1000; 0.1; 0.01 ; 0.001? How do you express the division of a decimal by 10; 100; 1000; 0.1; 0.01; 0.001? 42 * See page 57, for Explanation of the Use of the Drill Tables. 300. We measure the length of anything by applying to it a line of known length, as 1 foot, 1 yard, and finding how many such lengths it contains. The line of known length so used is a linear unit. 301. The length of a line is reckoned in linear units. 302. In measuring length we employ the mile (m.), rod (rd.), yard (yd.), foot (ft.), and inch (in.). These are the units of Long Measure. NOTE I. The standard unit of length is the YARD. From this the other units of length are derived. NOTE II. For surveyors' and mariners' measures, see Appendix, page 306. 303. Oral Exercises. a. How many inches are there in 1 yard ? in 2 yards ? in half a yard ? in a quarter ? in an eighth ? in a sixteenth ? b. What will it cost to grade a mile of road at $1 a rod ? c. What is the length in feet of a hall that is 15 yards 2 feet long? d. How many feet in the length of a fence 5 rods long? e. One eighth of a mile is sometimes called a furlong. How many rods in a furlong ? |