9. Which of the following gives all of the reciprocals correctly for the numbers 29, 375, 0.0027, and 0.179?

a. 0.0345, 0.00267, 370, 5.59

b. 0.0345, 0.00333, 430, 6.41

c. 0.0455, 0.00333, 370, 5.59

d. 0.455, 0.00267, 370, 6.41

e. None of the above

10. A steel plate 4-inch thick weighs 10.2 pounds per square foot. How many pounds does a piece 1⁄2-inch thick, 7.4 feet wide, and 9.6 feet long weigh?

a. 145

b. 362.5

c. 1,265

d. 1,450

e. None of the above

What is the

11. A mason can lay 947 bricks in an 8-hour day. average number of bricks he can lay per minute?

a. 0.507

d. 2.02

b. 1.263

c. 1.97

e. None of the above

12. An object travels 10,560,000 feet in one day. How many miles per hour does it travel?

Written Assignment

1. Using the examples in your text as a guide, explain how to find

the result of

40.3 0.0382

The CI scale should be used and the ex

planation should include the location of the decimal point.

2. Using the examples in your text as a guide, explain how you would find the product of 1.797X353X0.00648. This should be done by using the CI scale to its best advantage and the explanation should include the location of the decimal point.

3. Using the examples in your text as a guide, explain how you would find the answer to This should be

27 436X0.00327X795

done by using the CI scale to its best advantage and the explanation should include the location of the decimal point.

4. Use the CI scale wherever practicable to find the result in each of the following problems. Write both the original numbers and your answers on the lesson sheet.

a. 37.95X0.0317807

b. 10,006X275X96.4

c. 439X0.000791X38

d. 18.86X0.595X17

e. 1.93X0.495X0.0033

5. Use the CI scale wherever practicable to find the result in each of the following problems. Write both the original numbers and your answers on the lesson sheet.

6. How many cubic yards of concrete are needed to pour a 4-inch slab covering a rectangular floor 8 feet 9 inches by 27 feet 3 inches?

7. A steel plate 2-inch thick weighs 20.4 pounds per square foot. How much does a piece 1-inch thick weigh if it is 8.9 feet wide and 11.3 feet long?

8. In an 8-hour day a machine knits 505 pounds of yarn. What is the average number of pounds the machine knits per minute?

9. If a car travels at 72 miles per hour, how many feet per second is it traveling?

10. What is the smallest volume in which you could pack 180 boxes each having outside dimensions of 10 inches by 3.7 feet by 1.3 yards? Give your answer in cubic feet.

Lesson 11

Review

You have now studied all of the scales contained on the Mannheim slide rule furnished by USAFI except the log scale. If you have some knowledge of logarithms or wish to study them when you complete this lesson, study lesson 12, which is optional.

Although the operations used in this lesson will not be new to you, it is, nevertheless, a very important lesson. As you studied the preceding lessons, you spent your entire time studying just one or two scales. Now you will have an opportunity to solve a wide variety of problems in a single lesson using all of the scales of the Mannheim slide rule. This means you will need to read each problem carefully before deciding which scales to use to solve the problem most efficiently.

Text Assignment

Chapters XIII and XIV, pages 231–239.

Study Notes

Page 231. Check your slide rule as suggested in this chapter to determine if it is accurate and easy to operate. You will probably find that an inexpensive slide rule fails to meet all of these accuracy checks. Often the sine, log, and tangent scales are more inaccurate than the other scales. If you use a slide rule often, you will probably wish to purchase one that is better constructed than that furnished by USAFI. Before spending money on an inaccurate slide rule, be certain to give it the checks described in the text. Occasionally, even an expensive slide rule will have a flaw. Also, many of the more expensive slide rules are adjustable and this chapter will serve as an excellent guide for adjusting such rules.

Page 235. The section on good judgment deserves special attention. Whenever you solve a mathematical problem, regardless of whether or not you use a slide rule, always take a good look at your solution to determine if it appears reasonable in terms of the original data. For example, a misplaced decimal point, particularly in a money problem, will often result in an unreasonable answer that can be spotted by a visual check. Of course, there are some errors that will be difficult to detect by a visual check of the final answer. A mistake such as setting 901 as 910 cannot be easily detected.

When solving a wide variety of problems in which different scales are used, errors are often made in setting and reading numbers. To avoid this, care must be taken to observe the number of spaces in the section of the scale being used. For example, there are only 5 spaces in each section of the K scale between the numbers 6 and 10. Consequently, a number such as 6.3 is often incorrectly located or read on the K scale as 6.15.

Page 236. It is pointed out on this page that the slide rule can be read more accurately than the smallest unit space by estimating to one-tenth of one space. While this is true, do not attempt this unless you have first checked the spaces on your slide rule to be certain they are marked accurately. It is of no value to estimate that you are three-tenths of the way between two lines when the lines are not the correct distance apart.

Pages 237-238. A summary of rules for locating the decimal point is given on these pages. Suppose for a particular operation you forget the rules for locating the decimal point. You can easily figure them out for yourself by solving a few very simple problems. Let us say you have forgotten the rules for locating the decimal point when multiplying with the C and D scales. Try the problem 2 X 4 = 8. The slide extends to the right for this operation. The sum of the digit counts for the original numbers is 1+1=2. However, since the answer 8 has only 1 digit, this operation means you subtract one from the sum of the digit counts of the original numbers to get the answer. Now try the problem 2X9=18. The slide extends to the left for this problem. The sum of the digit counts for the original numbers is again 1+1=2. This sum is the same as the number of digits in the answer, 18. Thus, you can formulate the two rules for locating the decimal point when multiplying with the C and D scalesone rule to use when the slide extends to the right and the other to use when the slide extends to the left. In this same manner you can formulate the digit count rules for other operations.