Page 43 - Appplied Mathematics for the Petroleum and Other Industries, 5th Edition

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Answer Key

Problems involving decimals may have discrepancies in their answers—for example, the problem involving the num-
ber of fans needed to change the air every 3 minutes in a given area. Possible answers are 4.053, 4.05, 4, or 5 fans,
depending upon the practical application. Four fans will not quite do the job. Also, with 4 fans, there is no standby
for emergency. The engineer would probably call for 5 fans. If the specification for a change of air each 3 minutes
included a factor for safety, perhaps 4 fans would suffice. Obviously, it is not possible to install 4.053 fans, but that
is the solution to the problem to three decimal places. At this point, judgment enters the picture.
Problems involving only whole numbers are precise in the results obtained. Many problems in fractions cannot
be worked to a final answer. Rounding off fractions to whole numbers, to one place, to two places, and so forth will
change the end result. For example, using pi on a calculator instead of 3.1416 will slightly alter an answer. Using
rounded-off conversion factors as given in the chapter tables will result in answers different from those solved by
using the exact conversion factors given in Appendix C. These answers may vary considerably if large quantities are
involved.
As a user of this manual, you should compare your answer with that given, and if there is a difference, check
your work. If it is not in error, then you might ask, “How can this difference be accounted for?” or “Is my answer
satisfactory although perhaps not exact?” If it is satisfactory for the purpose you had in mind from the beginning,
then it should be acceptable. However, you should always be able to explain how the difference arose.
ANSWERS TO PRACTICE PROBLEMS

1. THE NUMBER SYSTEM Common Fractions, pp. 19–20 8. /16"
5
9. 7'5 /16"
9
6
Whole Numbers, pp. 13–14 1. a. /64 21
b. /16 10. /64"
12
1. a. 5,000 14
b. 110 c. /16 Mixed Numbers, pp. 23–24
7
c. 30 d. /8 1 6 1. 40 hr
4
d. 10 2. a. /8, /8, /8 7 2. 17 /16"
15

4
2
2. a. 42 b. /32, /32, /32 17 4 62 3. 20 /32"
29
19
56
22
b. 361,000,000 c. /64, /64, /64, /64, /64, /64 4. 12 /4 hr
1
60
3
62
c. 27,051,289,000 d. /64, /64, /64 5. /32"
5
1
d. 20,400,502,000,000 3. a. /2 6. 45 /8"

7
3
3. a. four thousand, six hundred b. /8 4
1
b. seventy-eight thousand c. /8 7. 764 /13 bbl
5
c. eight million, six hundred d. /6 8. 10
1
thousand 4. a. 1 /2 9. 21
5
d. eighty billion, seven hun- b. 3 /16 10. 1,100 bbl
7
dred forty million c. /32 Decimal Fractions, pp. 31–32
43
4. a. 953 d. /64
Petroleum Extension-The University of Texas at Austin
5
b. 236 5. a. 5 /8 1. a. three thousandths
7
35
c. 1,281,150 b. /160 or /32 b. six hundred twenty-five
1
d. 6,485,381 c. 1 /10 thousandths
5
5. a. $3,520 per month d. /18 c. one hundred twenty and
$42,240 per year 6. 30 bbl four hundredths
b. 17 hr 7. Jones: $28, 125 d. eight and three thousand,
c. 1,090 ft Smith: $14,062.50 seven hundred, forty-five
d. 4,811 ft White: $32,812.50 ten thousandths
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