Exact Values - Pointless?

Question

Ok, firstly let me start by saying that I am not one of those little kids that think maths is pointless etc etc. I am actually a university student and I do pretty well at maths and enjoy maths.


Question: Is there any real point in finding exact values? Ok, I get that it makes the answer nice and neat. But whenever someone engineers something, they will not work in exact values. They will put it into a calculator and get an answer with a few decimal places.

We can find the exact value of sin(105) by trig formula but does anyone actually care about the exact value?

Answer 1

If you round numbers in intermediate steps of a particular calculation your final answer (the result) may be accurate to very few decimal points or may just be plain wrong. The rounded values are based off of the exact values. Some applications need more precision then others. If you only knew the accuracy of a number up to 2 decimal points but what you were applying you calculations to required a number to be accurate to 5 decimal places, you would be in trouble.

Answer 2

In certain problems, it is necessary to use exact values, primarily for trigonometry function, because a little rounding can mess up the entire answer later on. Sometimes some values have to be rounded but sin 105 is not a number that needs to be rounded. I remember I answered a math problem a few weeks ago that I had to round and when I finished explaining the problem, I check the answer in the calculator and the answer was different by .08. .08 isn't a whole lot but it is still a considerable amount of error. If the answer can not be an exact value, it is better to have it rounded to at least 4 decimal places or approximate the value at the very end of the problem.

Answer 3

I would say you'll never have to use formulas such as the one to find sin(105) and usually you can just put it in the calculator and you're good to go. Your answer will be relatively exact, etc. But I think the issue comes when multiplying the numbers. 3.14 is a good approximation of pi. But when you start working with that number, multiplying it, squaring it, etc, your results will become less and less accurate with each operation. Pretty soon you will be fatally far away from the true value. Herein lies the idea of an exact number. With exact numbers there is never any question. If its a non-repeating non-terminating decimal (such as sin(105)) you can truncate it after all of the math is finished.

Answer 4

Hey there! I'm a student as well, I'm currently double majoring in Mathematics and Physics at Arkansas State University. This is like asking why is there bread on a sandwhich lol exact value's in trig (since you reffered to it:) ) would be like 7pi/4. You don't actually break it down and get .8666 whatever it is, it ends up being lengths of sides. Exact values give you different applications in math, yes, you can put something in a decimal form as long as it abides by the domain of the function of course, but its easier for us to put some things in exact value, double angle identites, if there were no exact values, we'd have to sit here and take all the extra time to figure out with the x,y is so we can actually to the identity! But these are practical trigonometric uses...hope this at least gave you an idea, have a good day bub! Good luck in school!

Answer 5

Mathematics requires exact values. i.e. it's bad practice to leave a number in the form 1/sqrt2.

How can we divide by sqrt2 when we don't know its exact value.

How can we write a = b unless we have exact values.

Engineering does not require exact values, the precision and accuracy reqirements are normally given in advance.

Exact values are required for encryption and so are extraordinarily large prime numbers.

Answer 6

When you are performing calculations, you always want to use the most precise values you can, i.e. the correct number of significant digits. Lack of precision in calculations early on can lead to massive errors at the end. It works like the butterfly effect, where an error of, say .001 early on in a very long calculation, can lead to an error that can be measured in many orders of magnitude.

Answer 7

each and each and every human life has a reason - the movements of its moms and dads - yet that does no longer propose it has a purpose of any style in its own excellent. some human beings sense the favor to seem for meaning in an really meaningless lifespan so might want to latch onto some thing they call a purpose yet their life might want to have began and ended besides, without that claimed purpose. The 'purpose' isn't any more suitable than a fabrication, an indulgence of ego in case you want. We did not ask to be the following yet the following we are. we'd want to besides make the finest of it and, as a thanks to optimise the soundness of rewards/expenses, that suggests residing in a way that contributes to the collective pursuits of society. it is nevertheless no longer a purpose - in simple terms an orderly framework in which we play out our years. If we opt for to fill our time with interesting activities, it truly is fantastic. If we opt for to do good works for the convenience of others or the aggrandisement of ourselves, it truly is fantastic too. If it makes human beings sense more suitable advantageous to call that a own, chosen purpose, it truly is fantastic. it continues to be only a use of life fairly than a purpose for it. no longer each and every thing has a purpose.