I want to say thanks for putting up this website. I found a lot of great shortcuts for my students here. I had figured a lot of them out on my own but many of the ones you figured out were stated a little clearer than mine or the method was a little easier.
I have a question on some of the estimation problems, mainly the division ones. I would appreciate a little help in explaining stuff like this:
131452/279
I have always had a weak spot when it comes to division, which I think is funny for a math teacher. I am just having trouble rounding for the estimation. Any help would be greatly appreciated.
I also forgot how to convert from rectangular to polar and vice versa. Any help on that would be greatly appreciated.
Any help would be greatly appreciated. Again, excellent website and best of luck to you in this endeavor.
Thanks for you kind words and for your enthusiasm in number sense. I will do what I can to help.
The estimation problem you gave is a tough one. The reason it is so tough is you have very little room for error. The very frst thing I would do is to find out how many digits the answer is going to have. There are 6 digits in the numerator and 3 in the denominator. Since 279 cannot divide into 131 at least once we simply subtract 3 from 6 and get 3. This is how many digits the answer will have. (If this is confusing you can see the website under approximations, for more details).
Now comes the really hard part. We have to decide how to round to make this problem easier. Just because I have done so many of these types of problems, I can guess that it would probably be safe to use 140000/300. You want to make the denominator easy to divide by. The only problem is you had to add quite a lot to it to make it 300. For every 1 that you add you have to add another 279 (which is approximately 300) to the top. I added almost 20 which means I need to add about 6000 to the top. You can use 137452 / 300 if you want, but when using this trick or method you will always be under the correct answer. So it is safe to round up to 14000. In fact, you will probably get an answer closer to the real answer. (*Notice, you have a lot of leniency with the numerator because changing it a few numbers really doesn't change the answer that much. That is why I changed to 14000. If you change the denominator though, it will have a big impact on the answer.*)
The truth is, every one has there own method of doing these. This took a long time to describe, but if you put it in practice it really doesn't take that long to do. It just takes lots of practice.
As far as Polar Coordinates to Rectangular Coordinates you can use :
x = r cos P, where p = pheta or the angle
y = r sin P, where p = pheta
For Rectangular Coordinates to Polar Coordinates you use:
r = sqrt(x^2 + y^2)
p = atan (y/x)
If you need more help on this or want to know why these formulas are what they are, just write back.
P.S. Don't worry about having a weak spot in division. You can ask my wife, I have a weak spot for adding and subtracting. I can multiply in my head better than I can add. That is scary coming from a math major.
i would find out the how many digits are in the answer first, then do 13100/28 and get about...470 or so, but again, it's a personal thing...some people are better with their own tricks...i hope this kinda sorta helped...(you didn't really ask for my reply and i just answered randomly...)
