Fun Math Trick! Squaring Numbers Near 100.
A neat way to square numbers near 100 without having to multiply it out the long way!
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Duration : 0:3:10
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Fun Math Trick! Squaring Numbers Near 100
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As much as I hate …
As much as I hate to admit it, you’re right. 0.999… can’t be graphed.
You’re arguments; however, have lead be to the point of saying that no irrational number can be placed on a graph. 0.333… allegedly equals 1/3, but I would argue that it never truely reaches 1/3. it is simply the closest decimal in existence to 1/3, and so we say the two are equal. Similarly, 0.999… is infinitively close to 1, yet not equal. 1 is already a decimal. When would one ever need to use 0.999… rather than 1?
Um no, you are …
Um no, you are assuming the two are different. Since they are in fact EQUAL 0.999…. CANNOT equal x in your example. You can enter 0.999999999999999999999999999999 in the graph, but the … means the 9′s never stop, EVER.
Wow, that’s an …
Wow, that’s an interesting trick.
I came up with a formula for easily squaring double didgets in one’s head.
x^2=(n^2+n(x-n)+x(x-n))
x is the number that you want to square, and n is the a nearby number that you already know the square for. If x=57, then n might equal 60 or 50 because it’s easy to find their squares. (3600 or 2500)
It may look complex, but it’s really easy to figure out and with a bit of practice it’s easy to remember and you can amaze your friends.
100 has only 2 …
100 has only 2 extra zeros, so when you add the square of the difference between you’re number and 100, only the last 2 didgets of that square remain the same. Any didgets before that are carried over to their appropriate places and added.
You make an …
You make an interesting point, but I wouldn’t go so far as to say that 0.999…=1 because on a graph if x=1 is a hole or an asmptote, 0.999… can equal x, but 1 can not.
don’t you mean …
don’t you mean 3.9999…=4? Or that 2.999… = 3? LOL I still understand what you meant
For two numbers to …
For two numbers to be different you would be able to find another number in between them. This cannot be argued. 2 and 2.1 are different numbers because 2.01 is between them. 2 and 2.01 are different because 2.009 is between them.
So a simple proof that 0.999… = 1 is that there is NO number in between the two of them, because the 9′s go on forever and never stop, NEVER stop. So they are the same number.
The same logic means that 1.999… = 2, 3.999… = 3 and so on. This is mathematical fact.
when and how do you …
when and how do you know you have to carry a number??
cool
cool
Now that’s just a …
Now that’s just a retarded proof. Just because the preceding approximations follow a seemingly similar pattern, it will never make 9/9 = 0.9999. It’s exactly 1.
Whoa… these …
Whoa… these little tricks still blow me away. Nice.
LOL….
0.999… …
LOL….
0.999… does equal 1, because if you follow the pattern: 1/9=0.11111….., 2/9=0.22222…. and so on, then 9/9=0.999999999…=1
Ownage
Ownage
Very neat trick. I …
Very neat trick. I squared the numbers on my calculator and tried them the way PatrickJMT did it, and they were the same.
It doesn’t matter …
It doesn’t matter what anyone “believes”, it’s simply a provable mathematical fact.
Hey, no …
Hey, no offensiveness at all, many people don’t believe 0.999… = 1, and I am one of them. No doubt, Patrick is a smart guy, that’s why I would like to know his point of view of 0.999… = 1. Just thought he might be able to show a proof of 0.999… =1 video on that.
I’m not Patrick, …
I’m not Patrick, but I believe I can answer that. He’s not an idiot, so yes. It is a provable mathematical fact..
No, I’m saying, how …
No, I’m saying, how often do you really need to find the square of a number near 100? Not very often, and when you do, it would most likely be just a small part of a bigger maths problem. So you would most likely have a calculator anyway, in which case it’s much quicker and easier to just punch in the numbers. Calculators, and computers are so ubiquitous nowdays. If you are the type of person who constantly need to do a lot of maths, you WILL be carrying a tiny calculator ALL the time.
what do you mean? …
what do you mean? do you mean to say that relying on a calculator is practical? because you would be wrong in so many ways.
Hey Patrick, Do you …
Hey Patrick, Do you believe 0.999… = 1?
Lolx…. a fine …
Lolx…. a fine thing.
thanks a lot …
thanks a lot patrickJMT! You rock
hmm! its …
hmm! its interesting
pls keep posting math tricks
Neat trick, though …
Neat trick, though its practical usefulness is kinda dubious.
me too : )
…
me too : )
ultimately, i am a lazy guy – this helps me be more lazy (ie, faster!)