Maths question

[Taffy_is_a_Taff]

what is 2 to the power of 10000?

my fancy calculator just says "inf".

[drone]

According to Windows Calculator:

1.9950631168807583848837421626836 x 10^3010.

[BDC]

what is 2 to the power of 10000?

my fancy calculator just says "inf".

Seems pretty close to me. That's 2 doubled 10,000 times, so probably a bigger number than atoms in the universe or something.

[Taffy_is_a_Taff]

cheers people, it is an insane number, it was one of those ridiculous little bits of homework.

[Dutch_guy]

why would anyone want to know what 2^10 000 is ?

[Taffy_is_a_Taff]

why would anyone want to know what 2^10 000 is ?

I have no idea. Apparently writing "inf." is not good enough.

[Duke Malcolm]

pff. Ignore your teacher and just write "too big for my calculator"

[Taffy_is_a_Taff]

According to Windows Calculator:

1.9950631168807583848837421626836 x 10^3010.

thanks for alerting me to the fact that windows calculator has a scientific calculator. I honestly never knew.

[Taffy_is_a_Taff]

pff. Ignore your teacher and just write "too big for my calculator"

bah, I tried that, it was the only red ink on the paper. He handed it back to me and suggested I fix it so that I could get 100%.

[drone]

thanks for alerting me to the fact that windows calculator has a scientific calculator. I honestly never knew.

Here at work, it's a godsend. I'm too lazy to do hex-to-decimal conversions in my head.

[Papewaio]

According to Windows Calculator:

1.9950631168807583848837421626836 x 10^3010.

If the universe was a sphere of water with a radius of about 15 billion light years, weighing 1000kgs per cubic meter, I estimate that it would contain something in the order of 1 x 10^101 molecules of water.

2 x 10^3010 is an absurb number, so what is the point in knowing it?

[ajaxfetish]

Seems pretty close to me. That's 2 doubled 10,000 times, so probably a bigger number than atoms in the universe or something.

Of course, you could argue that it's just about as close to infinity as 4, or 1/2, or any other finite number.

It is pretty big though, still.



Ajax

[Taffy_is_a_Taff]

If the universe was a sphere of water with a radius of about 15 billion light years, weighing 1000kgs per cubic meter, I estimate that it would contain something in the order of 1 x 10^101 molecules of water.

2 x 10^3010 is an absurb number, so what is the point in knowing it?

I'd love to know too. To prove that we can use a calculator?

[Reenk Roink]

We should put our ORG heads together and come up with a new mathematical system...

...............

[Taffy_is_a_Taff]

I'd like a system that deals with fractions better than those generally in use.

[Uesugi Kenshin]

Okay, here's my suggestion. Don't teach people that don't want to be taught math past exponents, quadratics and the beginnings of imaginary numbers. Most students here don't get to that, much less past it. And I certainly will never use what I am learning now ever again, except in classes of course.

I'd rather be slightly unbalanced than have a chance to get a C in Honors pre-calc....

[Duke of Gloucester]

I don't know. I am assuming that your maths teacher knows that you can't do that sum on a standard calculator and is expecting you to use some maths to work out this answer. How about:

2^10 = 1024

so 2^10000 = 1024^1000
= 1000^1000 x 1.024^1000
= 10^3000 x 1.024^1000

Now 1.024^1000 can be done on a normal calculator. It equals 2.00 x 10^10 to 3 sig. fig..

Therefore 2^10000 = 2.00 x 10^3010 calculated on a normal calculator using a little ingenuity.

[ajaxfetish]

And now I feel the effects of not having taken a math class in the last five years. When I was taking AP Calc I was on top of the world; now the good Duke's post is complete gibberish to me.



Ajax

[Ironside]

2^10000= 10^(lg2*10000)= 10^3010.2999566398119521373889472449
If your teacher doesn't like that answer

pick up the decimals of lg2*10000=3010.x

so you get 10^0.x = 1.9950631168807583848837421626836

Thus you get 1.9950631168807583848837421626836*10^3010

Haven't anyone here learned to count with logaritmes?

[Franconicus]

If the universe was a sphere of water with a radius of about 15 billion light years, weighing 1000kgs per cubic meter, I estimate that it would contain something in the order of 1 x 10^101 molecules of water.

2 x 10^3010 is an absurb number, so what is the point in knowing it?

Math is an abstract science. It is a logical construct. By a funny accident it can be applied to reality. Maybe the big creator loves abstract things too!

Anyway, no number is close to inf. And no number is meaningless. Just take the philosopher's approach: You can imagine this number, ergo it is!

Did you know that there is laugh 2,3,4 but no laugh 1? Strange! I think mankind could learn a lot if it could only find out why

[doc_bean]

what is 2 to the power of 10000?

my fancy calculator just says "inf".

2 to the power of 10000 is 2 to the power of 10000 obviously, what's the point of writing something that can be so elegantly (and correctly) expressed in a binary system in a decimal one ? I really don't get why he would ask something like that.

You don't normally use scientific calculators ? We've used them since grade 10 (I think, might have been 9).

Okay, here's my suggestion. Don't teach people that don't want to be taught math past exponents, quadratics and the beginnings of imaginary numbers. Most students here don't get to that, much less past it. And I certainly will never use what I am learning now ever again, except in classes of course.

I'd rather be slightly unbalanced than have a chance to get a C in Honors pre-calc....

I don't think everyone learns about imaginary numbers, iirc here it's only taught at the 'higher' education levels or in the more technical ones. I think they don't even see them in high School in the Netherlands.

[Taffy_is_a_Taff]

2 to the power of 10000 is 2 to the power of 10000 obviously, what's the point of writing something that can be so elegantly (and correctly) expressed in a binary system in a decimal one ? I really don't get why he would ask something like that.

You don't normally use scientific calculators ? We've used them since grade 10 (I think, might have been 9).

It was a miniscule part of an assignment, I don't know why they wanted it more expanded.

We do usually use scientific calculators, I have misplaced my very nice one and I did not know about the one in windows.

[Ironside]

2 to the power of 10000 is 2 to the power of 10000 obviously, what's the point of writing something that can be so elegantly (and correctly) expressed in a binary system in a decimal one ? I really don't get why he would ask something like that.

You don't normally use scientific calculators ? We've used them since grade 10 (I think, might have been 9).

Can yours handle numbers in that size though? My can only get to 10^100-1 and I've seen up to 10^1000-1 but not larger.

Never known about the science calculator in Windows either.

[Vladimir]

Haven't anyone here learned to count with logaritmes?

Ok I barely know how to even pronounce "logarithm" and you misspell it?

[Duke of Gloucester]

2^10000= 10^(lg2*10000)= 10^3010.2999566398119521373889472449
If your teacher doesn't like that answer

pick up the decimals of lg2*10000=3010.x

so you get 10^0.x = 1.9950631168807583848837421626836

Thus you get 1.9950631168807583848837421626836*10^3010

Haven't anyone here learned to count with logaritmes?

This is a better method, because it will work with any number, whereas my suggestion only works with powers of 2.

And now I feel the effects of not having taken a math class in the last five years. When I was taking AP Calc I was on top of the world; now the good Duke's post is complete gibberish to me.

And I have not done a maths course for 23 years. Is there a smug smiley?

[doc_bean]

Can yours handle numbers in that size though? My can only get to 10^100-1 and I've seen up to 10^1000-1 but not larger.

You're right

[Papewaio]

Math is an abstract science. It is a logical construct. By a funny accident it can be applied to reality. Maybe the big creator loves abstract things too!

Anyway, no number is close to inf. And no number is meaningless. Just take the philosopher's approach: You can imagine this number, ergo it is!

Math isn't that abstract... some of the greatest mathematicians are those who come from the physicists... calculus etc

If anything it is rooted in nature and then applied to abstract ideas, occassionally coming back to touch the natural world.

And I wouldn't define maths as a science. It is a tool used by scientists. But science is the act of describing natural phenomena by natural means. The very ability for maths to be abstract of nature means that it is not science.

Did you know that there is laugh 2,3,4 but no laugh 1? Strange! I think mankind could learn a lot if it could only find out why

last laugh is on you. Laugh1 doesn't have a 1...

Ironside-san ... that is the superior method as it more universal in approach.

[Uesugi Kenshin]

I don't think everyone learns about imaginary numbers, iirc here it's only taught at the 'higher' education levels or in the more technical ones. I think they don't even see them in high School in the Netherlands.

Same here, unfortunately since I am reasonably good at math I have to take three years of it. Which is enough to throw me head-first into imaginary numbers and funky quadratics with fractional exponents.

[ajaxfetish]

And I have not done a maths course for 23 years. Is there a smug smiley?

There ya go!

Ajax

[Alexander the Pretty Good]

Better yet, take the integral of f(x) = x^2 for the interval [0, 2^10000].

What does your calculator say about that?