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# CH-01 - Chapter 1 1 Using the given conversion factors we...

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Chapter 1 1. Using the given conversion factors, we find (a) the distance d in rods to be 4.0 furlongs 201.168 m furlong 4.0 furlongs = 160 rods, 5.0292 m rod d (b) and that distance in chains to be 4.0 furlongs 201.168 m furlong 40 chains. 20.117 m chain d 2. The conversion factors 1 gry 1/10 line , 1 line=1/12 inch and 1 point = 1/72 inch imply that 1 gry = (1/10)(1/12)(72 points) = 0.60 point. Thus, 1 gry 2 = (0.60 point) 2 = 0.36 point 2 , which means that 2 2 0.50 gry = 0.18 point . 3. The metric prefixes (micro, pico, nano, …) are given for ready reference on the inside front cover of the textbook (see also Table 1–2). (a) Since 1 km = 1 10 3 m and 1 m = 1 10 6 m, 3 3 6 9 1km 10 m 10 m 10 m m 10 m. The given measurement is 1.0 km (two significant figures), which implies our result should be written as 1.0 10 9 m. (b) We calculate the number of microns in 1 centimeter. Since 1 cm = 10 2 m, 2 2 6 4 1cm = 10 m = 10 m 10 m m 10 m. We conclude that the fraction of one centimeter equal to 1.0 m is 1.0 10 4 . (c) Since 1 yd = (3 ft)(0.3048 m/ft) = 0.9144 m, 6 5 1.0 yd = 0.91m 10 m m 9.1 10 m. 1

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CHAPTER 1 4. (a) Using the conversion factors 1 inch = 2.54 cm exactly and 6 picas = 1 inch, we obtain 1 inch 6 picas 0.80 cm = 0.80 cm 1.9 picas. 2.54 cm 1 inch �� �� �� (b) With 12 points = 1 pica, we have 1 inch 6 picas 12 points 0.80 cm = 0.80 cm 23 points. 2.54 cm 1 inch 1 pica �� �� �� �� �� �� 5. Various geometric formulas are given in Appendix E. (a) Substituting R 6 37 10 10 6 37 10 6 3 3 . . m km m km c hc h into circumference = 2 R , we obtain 4.00 10 4 km. (b) The surface area of Earth is 2 2 3 8 2 4 4 6.37 10 km 5.10 10 km . A R     (c) The volume of Earth is 3 3 3 12 3 4 4 6.37 10 km 1.08 10 km . 3 3 V R 6. We make use of Table 1-6. (a) We look at the first (“cahiz”) column: 1 fanega is equivalent to what amount of cahiz? We note from the already completed part of the table that 1 cahiz equals a dozen fanega. Thus, 1 fanega = cahiz, or 8.33 10 2 cahiz. Similarly, “1 cahiz = 48 cuartilla” (in the already completed part) implies that 1 cuartilla = cahiz, or 2.08 10 2 cahiz. Continuing in this way, the remaining entries in the first column are 6.94 10 3 and 3 3.47 10 . (b) In the second (“fanega”) column, we similarly find 0.250, 8.33 10 2 , and 4.17 10 2 for the last three entries. (c) In the third (“cuartilla”) column, we obtain 0.333 and 0.167 for the last two entries. (d) Finally, in the fourth (“almude”) column, we get = 0.500 for the last entry. 2
(e) Since the conversion table indicates that 1 almude is equivalent to 2 medios, our amount of 7.00 almudes must be equal to 14.0 medios.

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CH-01 - Chapter 1 1 Using the given conversion factors we...

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