# ATAT 110 Basic Mathematics # Week 13 ##### What This week we will explore a few more applications of mathematics in aviation to prepare you for your continuing studies. ##### Why The skills we have covered so far are directly useful in many aviation situations. Your work on your fundamental mathematical skills along with familiarity with where and how to apply them will be important for your entire career. ##### Testing You will be tested on this material on the final test. ## Approach and Objectives By understanding the following topics, you will have achieved the learning outcome for this lesson. Consult your course outline for the learning outcomes and other details of this course. ### Course Learning Objectives - CLO 1. Perform operations with whole numbers and fractions. - CLO 2. Perform series of operations using the appropriate order of operations. - CLO 3. Perform arithmetic operations with real numbers, including those in scientific notation. - CLO 4. Compute and simplify powers and roots of signed numbers. - CLO 5. Solve linear equations in one variable. %%whatever the fuck that's supposed to mean. I think solving for a variable qualifies, so there.%% - CLO 6. Apply percent and percent conversion in practical problems. - CLO 7. Use imperial and metric units and unit conversions as they relate to physical quantities involved in problem-solving. - CLO 8. Solve aviation related practical problems involving ratios and proportions. ### Main Topics - [[T110T SSGW06#Rulers|Rulers]] - [[T110T SSGW06#Ruler Manipulation|Ruler Manipulation]] ## Rulers %%[[T110T SSGW12#Rulers]]%% You will use a ruler or other similar measuring devices in many aviation scenarios. You must be fluent in the use of fractions to make good use of rulers, but luckily, this is a small subset of the possible fractions, and therefore, quickly committed to memory and ease of use. ### Imperial Units If a ruler is based on inches, the fractional derivation is achieved by dividing in halves to give us the following common subdivisions of an inch: $\frac {1}{2}, \frac {1}{4}, \frac {1}{8}, \frac {1}{16}, \frac {1}{32}$ Because of the limited space on a ruler and the importance of the lines being easy to read, labelling is often limited, and the lines themselves are used to determine the length you are measuring. The fractional calculations required are on you. The size of the lines on a nicely designed ruler will make it obvious to you when you are looking at a $\frac {1}{2}, \frac {1}{4}, \frac {1}{8}, \frac {1}{16}, or \frac {1}{32}$ division on the ruler. Usually the longest lines are the largest divisions.  A ruler like the one above would not be useful if you had to measure to a higher precision. More divisions would allow more choices for accurate fractions of the inch. Notice in this example how there is not a specific line length for the 1/8" division:  You may find yourself using a ruler that gives precision up to 1/32", and now the length of the lines can be quite helpful in determining a correct measurement. Notice in this example how there is not a specific line length for the 1/16" division:  Equivalent fractions are usually not given, and so if you need a length of 20/32", you would have to do the arithmetic yourself to realize you need to measure 5/8". ### Metric If a ruler is based on a metre, you can expect the subdivisions to be a little different. ![[Pasted image 20211011023714.png|350]]  Typically centimeters will be the base unit rather than inches, and the divisions will be by 10 rather than two. However a combination is often seen, as in the above cases where the first division of the centimetre is in half, and then by 10s, as indicated by the lines. It of course could be argued that this is truly a metric system, where the divisions are purely by 10, with the .5 mark indicated as a convenience. There are varying models of rulers, and some may meet your needs or preferences better than others. Some models of ruler are very accurate, but you may expect to pay more for such precision. For your convenience, some rulers use one edge for one measurement system such as imperial and the other for metric.  Some offer different scales on different edges.  Which ruler you use depends on the accuracy you require, the lengths involved, and your preferences. Shop carefully, rulers can get expensive. A quality ruler however, if well cared for, can last a lifetime. You could also print out a ruler from your browser [🔗](https://www.printablerulers.net/) in a pinch, or keep something like this in your wallet for emergencies:  %% #JB metric ruler example or two?%% ## Ruler Manipulation Using a ruler is fairly straightforward, but there are things that you must be well versed in to make proper use of this instrument. Of course, to measure an item, you would line up the zero mark at one end of the item, and note the closest line on the ruler at the other end of the item. You would note the nearest inch short of the measurement, and then by succession the lines in their decreasing length, then to the precision required:  Your knowledge of fractions would help you to determine the length. Will you convert all of the fractions to a common denominator and add? Or will you convert on the fly, and add 32nds? 1 + 16/32 + 4/32 + 2/32 + 1/32. Now this problem is rather straightforward. Our length is 1 23/32" Doing it on the fly is easier if you understand the math too. How did I convert 1/2 so quickly to 16/32? I want 32nds, so I divided 32 by 2. 1/8? Divide 32 by 8. Etc etc. But keep in mind, I will never be doing this with 14ths or 7ths or things like that. Just this subset that is in common use. You get used to it rather quickly, especially if you concentrate. What is the length of this object?  [[A Math|🅰]] Different is marking something for cutting or marking where you must find the correct length on the ruler, and then mark your material item. You would need to consider the precision of your writing or marking instrument, and you must watch out for parallax error. You would decide which line on the ruler to use based on your calculations, and your skill in "walking" the fractions to the required line. ### Parallax Error Because of the physicality of the ruler, that is, it's thickness, and the distance from the object being measured, you may make errors with rulers if your eyes are not correctly aligned. This type of error is called a parallax error. This is not an issue only with rulers. [[V Parallax Error|🎞]]  If you are in the electrical lab, and you are required to cut of a length of wire such that you can later cut it to specific equal lengths, you have some options. You can calculate using the separate measurements required or, you could just use the ruler and count off successive lengths according to your needs. Practice brings these techniques into your repertoire to make your work go faster and more accurately. Remember, if you measure material to cut, and you make a mistake, it could very easily be a mistake with a cost for wasted materials. Carpenters all know: Measure twice, cut once. They know it's easy to make a mistake when measuring. ### Other mathematical applications on Rulers The ruler can be used as a number line to aid in calculations. The visual representation may help you. If you must cut holes that are equidistant, that is equally spaced apart, within a fixed distance, you will have to use division calculations and then be able to find them on the ruler to mark your holes. Note that this method of having a scale from which to derive measurements of varying accuracy can be applied to other instruments as well, such as micrometers, torque wrenches, calipers, guages, and others. Be prepared to bring this knowledge to bear when you are introduced to these instruments and tools later in the program. Parallax errors are also possible with certain instruments. ![[Pasted image 20211011130634.png|350]] ## Mandatory Project 110 2 This mandatory project is a 10 question quiz where you will demonstrate your practical skills in calculating conversions. Refer to [[T110T SSGW10#Unit Conversions|this section]] for review on the required mathematical operations you will need to complete this Mandatory Project. Complete the MP 110-2 quiz in eCentennial to complete this MP. You have unlimited attempts to get 100% of the questions correct. ## Course Conclusion You may not assume that since this course is done your work to improve your math skills is also done. Surely you see now that these basic skills are used throughout the program in many aviation activities, and will be essential to your success as an AME apprentice. Best of luck in this program and in your aviation career! #JB