Well, now that the laptop I got for Christmas broke after a month, JUST as soon as I started my online classes again, I have limited online time, almost all of which is limited to my studies. It's finally happened, I'm at the age where real life is so prominent that I can't spend 5 hours a day on Overwatch, Fallout, Elder Scrolls, OR The Binding of Isaac. Truly dark times. Also I generally got sick of posting my thoughts on stuff here tbh, so yeah, probably wouldn't say I'd never get on Vizzed again, but not sure how many more times I'll even show up. Meh...

However, since it's been so long since I've been able to type out a 7 paragraph post about pumpkins or something, all my thought processes have been building up for a while, and today they were let loose. Now this isn't about people, it isn't about a game, it's about something that happened today... a 5 question test. Basically after getting the results on an exam, I flipped my lid and created a very large wordpad document to send to my teacher as an email. After I was done, I decided I would put it up somewhere. Somewhere being here. Cause I have nowhere else to go... sorry?

Note: This essay includes various topics concerning...
How to round decimals
What a significant digit is
How to launch the Mars NASA project
How fast a baby grows
The rarity and quality of gasoline
Me generally being an idiot

Enjoy?


Hello, I am currently taking your Algebra course, and I'd like to address a situation with a question I was presented with in my descriptive modeling and accuracy exam. There were 5 questions in total, and out of them, I got only 2 correct. When reviewing the ones I got correct, I was left perplexed at the ones which I got wrong and even the ones I got correct, to the point I started researching these questions in depth.

Question one was rather simple.

"During an alpine skiing event, the times of four skiers were listed below. Time is measured in seconds.
Skiers: Skier A, B, C, and D
Times in respective order: 114.36, 114.40, 114.44, and 114.48
If the stopwatch used was only accurate to the tenth of a second, which skier's time would be different from the others?
Skier A
Skier B
Skier C
Skier D"

Now I actually got this one correct, but after my second guess. I know that rounding decimals basically works like this...

Let's say we have 1.43, 1.48, and 1.45, a decimal number measured in the hundredths. If we were to round to the nearest tenth, we would be removing the inclusion of the right-most digit and keep the closest number to what it was with the hundredth. 1.43 would remain 1.4, while 1.48 would become 1.5. This is because overall, 1.48 would take a smaller change to reach 1.5 than if it were to go down to 1.4. When learning these rules, young students may have confusion with a decimal point of 5. Technically, 5 is usually the half point, 5+5=10, and the first numbers we learn in education are 1,2,3,4,5,6,7,8,9, and 10. However, 10 is a multi-digit number composed of a 1 followed by 0, so really, the order is more of 0,1,2,3,4,5,6,7,8, and 9. So generally, 5 can be considered just after the halfway point, in fact, no number really is the exact middle point from 0 to 10, so it's only the first half and second. So whenever rounding, it's important to remember a 5, when rounded, will be the next number over, so 1.45 would become 1.5. After reading the question, my immediate thought was skier A, as skier A was 114.4, not 114.3, generally making it look to have the same time as skier B and C. Before I selected skier A, I noticed that skier D was rounded to 114.5, not 114.4. After re-reading the question, I paid attention to the wording at the end of the final sentence, which skiers time would be different from the others. Since all other skiers were 114.4, and skier D was 114.5, this made the skier the odd one out, so that was the answer instead.

Next was question 2, the first question I got wrong and the reason I started looking into the dynamics of these questions to begin with.

"A rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the correct significant digits."

Rather than a multiple choice, this question was meant to be typed in a blank. We were looking at the area of a flat shape in square inches, which made it fairly simple, it wasn't like a 3D brick to be measured in cubic inches, but a 2D rectangle. Finding the area of any 4-sided shape is as simple as one multiplication, the length of one side multiplied by the width of either side connected to the first which is perpendicular. We already had the measurements, so all we needed was to multiply 9 and 4.25, getting an area of 38.25 cubic inches. When I got this wrong i really wanted verification. I used a calculator to see if I made a mistake, but it got the same answer. Then I copy and pasted the question itself onto the searchbar of a new tab to see if anyone else could answer this specific question. As the results loaded, I suddenly considered the last part, "round to the correct significant digits". It would seem I had to round the answer down, removing the decimals and just putting in 38. Ironically, the first result on the page was this...

http://openstudy.com/updates/52669c40e4b040e33d2d8039

This person seems confused at how he got the question wrong, and presents the question. The first answer just gave us the fact we knew could not be wrong, 9 times 4.25 is 38.25. Then the creator of the question replied that they hadn't used this number (unlike me) and instead they placed in the numbers 38, 39, and even 36. 39 didn't seem to be it, clearly due to the rounded decimal rule, but since 38 wasn't right either I can't blame them. 36 was probably put in after rounding 4.25 to just 4 and doing 9 times 4 instead. After another reply stating how the answer SHOULD be rounded, there were no more replies, and this question was made 3 years ago it seems.

Since these people only added to my confusion by not getting the correct answer I assumed should've been correct, I looked up the definition of significant digits.

Purplemath shows some basic rules of this...

The first 6 digits of pi, 3.14159, are all significant. They show that all digits are important to getting a precise answer. Of course, pi goes on infinitely, so a 6 digit pi isn't exact, but they show the appropriate measurement to be made concerning any answer factoring this number.

The only significant number in 1000 is the 1 in the beginning, as all the zero's after it are possibly placeholders, inferring this number was rounded to the nearest thousand, and no information on possible decimals is given. However, if we changed the number to 1000.0 all 5 digits would become significant, signifying that if a decimal is used, then if it was rounded it would probably have been to the nearest tenth, otherwise there would be no reason to have the decimal there. Presumably, the actual number could have been 1000.03 or something similar.

The number 0.00035 has 2 significant digits, as again, all zero's before are placeholders, but adding another 0 after 5 would make it the third significant digit, as the same rules above apply. Overall, any 0's before the first non-0 digit aren't significant, any 0's after the first significant digit are not significant until another non-0 is added, and once a decimal point is added, all 0's after the first significant digit are made significant, even past the decimal point. If no significant digits are present before the decimal, all 0's after the decimal are insignificant until a non-0 is added, and 0's after that will be significant.

With all of those rules in mind, let's refer back to this question we have not gotten correct as of yet.

"A rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the correct significant digits."

Now, I think I can safely say we don't even have enough information given to us to be sure as to the answer. The question has two numbers, both with 3 significant digits. Sure, the length can simply be called 9, but the fact that they included 2 0's after a decimal point means they are both significant as well. But wouldn't that make 38.25 the correct answer? Well my guess is since we know that isn't correct, and that 38 isn't either, then having 3 significant digits in the equation implies that the answer requires 3 digits as well. If that's right, that leaves us to round to tenths, or 38.3 for our answer. However, I'm still not satisfied about this, mainly because of the vagueness of the question itself.

Now often, in the scientific field, when creating formulas and equations, things need to be made precise. For instance, when a day comes where NASA wants to create a spaceship to reach Mars, which seems likely to happen, they need to determine how big their ship will be, how heavy it is, what fuel to use, how to contain it, how much to use, how fast the ship can travel and how long until it reaches top speed, how even the weight distribution is to keep it from shifting from its calculated course, keeping it clean as can be to prevent malfunctions and weight variance, then pick the exact time to launch by choosing a location, then predicting an ideal clear weathered day, possibly years after everything is ready, when the planet is in position, then the angle and speed to travel in order to reach escape velocity and move past the Earth's gravitational pull, also considering the effects of the slight nudge of gravity the moon provides, and making sure that the position in which you pass escape velocity sends the ship flinging where the planet Mars, anywhere from about 225 million km to 401 million km away depending on both our planet's year cycles and only has a radius of 2,106 MILES, will be positioned when the ship reaches its orbital path. During the trip, the ship needs all the mechanics to work as intended, from separating stages to making sure the landing on the surface of Mars goes without a hitch, and as long as the Mars project isn't a suicide mission, sending a few brave souls to another planet with no way back, the ship now needs to be able to launch AGAIN, escape Mars' escape velocity, which is fortunately weaker, but they still need to escape at the perfect angle to travel back to Earth and land safely again. These aren't even all the factors included, and each one is very difficult to pin down to a specific degree to cooperate with other factors to achieve the perfect journey to Mars, perfect being a relative term seeing as lots of things need to be maintained during the trip.

And here we're learning about dumbing down numbers.

I still have unfinished business with question 2, but how about we move onto question 3?

"Which of the following best represents the average rate at which infants grow in height during the first four years after birth?"

... this isn't an algebra question... this is parenting class.

So here we are, without a clear idea on the growth rate of humans, abandoning calculation and working out equations, and just using common sense. The options are 3 inches per month, 3 inches per year, 3 feet per month, and 3 feet per year. Ok, if during the initial 4 years of being born we go from a small newborn infant to Shaquille O'Neil in TWO years, we'd need taller highway signs, and 3 feet per month would be even more ridiculous. In just one year, we'd be 36 feet tall, never mind 3 more after that. Next, 3 inches per year. If we're looking at 4 years, that's only a whole foot in 4 years. However, just leveling with you, I'd assume a newborn is a little under a foot from birth, while I knew a 4 year old is well over 2 feet. So assuming this was wrong as well, I just selected the last one I didn't check. Shame on me for that, because the final answer was 3 inches per month. While not as ridiculous as 3 feet per month, one foot is 12 inches, meaning that 3 inches per month, 12 months a year, makes this answer the same thing as 3 feet per year.

After checking, an average newborn is actually 20 inches tall... which gives me a new perspective on how painful a mother's labor is... In fact, 3 inches per year isn't even an accurate measurement, it's the closest we received, but after looking at how big a 4 year old averagely is, that kid would be about 3 feet and 4 inches, almost TWO feet taller after 4 years. I mean, I can't really blame you, you have a degree in MATH.

Now when I saw question 2 was wrong, and that there were two other wrong questions, I still didn't really know what I picked for question 3, so I assumed I got question 3 right, and the final two were wrong, as they were basically that kind of "if this thing is this, then what is the other thing" two questions.

Question 4: Which of the following is the most appropriate unit to describe the time you can drive a car based on the amount of gas?
Minutes per gallon, because the independent quantity is the gallons
Minutes per gallon, because the independent quantity is the minutes
Gallons per minute, because the independent quantity is the gallons
Gallons per minute, because the independent quantity is the minutes

Question 5: Which of the following is the most appropriate unit to describe the rate of the cost of gasoline?
Dollars per gallon, because the dependent quantity is the gallons
Dollars per gallon, because the dependent quantity is the dollars
Gallons per dollar, because the dependent quantity is the gallons
Gallons per dollar, because the dependent quantity is the dollars

Here was my reasoning for question 4, minutes per gallon doesn't sound right, every minute is 60 seconds, time is constantly flowing, and in a grammatical sense, it's not like the gallons are using minutes. Gallons per minute are more like how many gallons are used each minute. Maybe not an entire gallon is burned within a minute, but a fraction of the gallon can be shown as a decimal amount per minute. As for independent quantity, I was pretty dang confused. Like I said, minutes are constant, so I assumed that since gallons of different fuel have different burn rates, and you don't even need to completely fill a car tank, gallons are too variable. So I chose minutes as independent quantities.

That out of the way, we got to question 5, and I was already at a bit of confliction. I already added a reasoning to the grammatically correct gallons per minute, but dollars per gallon mixed that up. I knew the correct way of saying it was dollars per gallon, but if I apply the idea I came up with to decide minutes were independent, then dollars are also constant like minutes. I mean Canadian dollars and American dollars are valued differently, but this is a FLORIDA virtual school, so any mention of dollars in math should be considered as our dollar system without having to add American before it. Now gallons seem to be the dependent quantity, and if they weren't the independent ones in the last question, that makes them dependent now right? So to recap, I decided on "Gallons per minute, because the independent quantity is the minutes" for number 4, and "Dollars per gallon, because the dependent quantity is the gallons" for number 5.

Now once I got the results of the test, I did research on question 2 to keep my sanity in check, whatever. Then seeing question 3 was wrong, I checked the records on baby growth to determine the inaccuracy of both my knowledge and the questions knowledge on something besides math... either way, it kept me occupied for a few minutes, researching these things to see how it was wrong, but it wasn't THAT big a deal yet. However, with two questions remaining, only one of them correct, I wanted to see what I got wrong. Then I noticed my big mistake, I chose the wrong response for my 4th question. Instead of picking the one where the independent quantity was minutes, I picked gallons as the independent quantity. That was the question that, I thought for a brief moment, was the reason I got an F instead of a D-. Then I scroll down, look at question 5... and flipped out. I didn't just pick the wrong answer for question 4, I also did for question 5, picking the dollars as the dependent quantity instead of gallons... except it was CORRECT.

AND THEN I DECIDED EVERYTHING I KNEW ABOUT LOGIC WAS A LIE.

Now let's address the elephant in the room, I was set on two answers for two side-by-side questions based on a single subject, and somehow chose different responses for both. I'm just going to say how I misclicked the first one, didn't notice the error while it was right in front of me the whole time while considering the answer for the next question, and then repeat the same error AGAIN, not notice AGAIN, and submit it, is probably some form of divine intervention. But the thing is even if I noticed and corrected my choices, the score would have been either the same or WORSE. If I rechecked all my answers, I would have gotten both question 4 and 5 wrong, and I only would have gotten the same score of 2/5 if I had also seen the answer I picked for question 3 and realized my mistake. But here's how I picked the most inaccurate answer for question 4. While I already knew the correct term was dollars per gallon for question 5, the correct term for question 4 is actually MINUTES per GALLON. Not only that, but the independent quantity actually is gallons, not minutes. Of course, this was AFTER I checked the right answer for question 4, before that, seeing as dollars per gallon and dollars being dependent quantities was CORRECT, I figured that time was independent, and gallons were neither dependent nor independent. I didn't even start trying to apply reasoning to this yet, rather than try and think how that would've been right, I checked for that answer and found out I messed up my minutes and gallons completely.

So if dollars are dependent, and gallons are independent, then what are the actual definitions? Well at first I thought independent quantities were quantities that weren't subject to variance, like the static length of time and value of currency, while dependent quantities often needed estimations to determine the exact statistics of how it would change, like in the case of gas, how long it lasts, how rare and dense it is, etc. Well are you ready for the definitions? Independent and dependent quantities are directly related to independent and dependent variables, which are, respectively, variables that are not affected by other factors, and variables that are. Some examples are as follows...

If someone travels x distance to reach a place, and were to move a distance of y per hour, the independent quantity is the time and the dependent one is the distance.

Filling a pool with a hose at x gallons per minute, the independent quantity is time, and the dependent one is the water.

If you put x invitations in an envelope per minute for a party, the independent quantity is time, and the dependent one is the envelopes.

If you're selling shirts for x dollars per shirt, the independent quantities are the shirts and the dependent one is the amount of money earned.

Notice how time seems to be the independent quantity most of the time? Not this time, the time until the gallon runs out is considered dependent on just how good the fuel is, making the quality of the gallon independent due to the chemical reaction occurring in the fuel determining how fast it burns up. However, if you want to apply logic... something I normally can't be trusted with it seems, there's a bunch more dependent and independent quantities, like the model of the car, how efficiently it uses the fuel, a variable which changes over time as the car gets older and wears itself down, so yeah, the gallon is independent so long as we ignore THAT. As for dollars being dependent quantities, the amount you pay is also dependent on the quality and rarity of the fuel you buy... and rarity itself is dependent on how much of something is on our planet and how easy it is to get.

So now here I am, a good 2 and a half hours later, and with this essay I made to verify all my thoughts on a 5 question test. I'm not done yet though, because there's still one more thing I can check... do we have the answer to question 2? I'm going to restart the test, and if the question is still there, I'm using 38.3 as my answer. If it STILL isn't correct, then for the love of god, please tell me how this works, and then tell me why the rules dictating how it works exist.

So I took the test again, and now that I know how the test thinks, I got 100 percent. I got questions 1-3 again, but new examples instead of what I got for questions 4 and 5. So yes, 38.3 was right. I'm still not happy about it though, but it was right, and now I have a B in this class.

... so yeah, this is what happens when I can't play videogames for a while and have limited access to the internet.