10! - NumberphileYouTube↗  IA↗(long shot)
Science & Technology  677.8K views 14K likes 299 dislikes   28 May 2012
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OK, so today we've got a little
Hoy trataremos sobre una pequeña
mathematical nugget for you.
joya matemática.
I'm going to talk about 10 factorial.
Voy a hablar sobre el 10 factorial.
So 10 factorial is what you get when you multiply the
10 factorial es lo que obtienes al multiplicar el
numbers 10 times 9 times 8 times 7--
número 10 por 9, por 8, por 7,
and you go all the way down, times 2, times 1.
y continúas multiplicando hasta el número 1
How big is 10 factorial?
¿Cuánto es 10 factorial?
On your calculator you will find a little bottom with an
En tu calculadora puedes encontrar un pequeño botón con una
exclamation mark after it.
exclamación
There we go.
Vamos allá.
That is how big 10 factorial is.
Este es el número 10 factorial.
Let's write this down.
Vamos a escribirlo aquí abajo.
3,628,800.
Now what I want to talk about is 10 factorial seconds.
Ahora me gustaría hablar sobre 10! segundos.
Now, how long is 10 factorial seconds?
Ahora, ¿Cuánto es 10! segundos?
All right, so 3,628,800 seconds.
Bien, pues 3.628.800 segundos
How long is that?
¿Cuánto es eso?
Well, it turns out to be exactly six weeks.
Bueno, pues resultan ser exactamente 6 semanas.
Let me show you.
Déjame que te lo enseñe.
We've got 10 factorial seconds, so how
Tenemos 10! segundos, así que
many minutes is that?
¿Cuántos minutos es eso?
There are 60 seconds in a minute, so I'm going
Hay 60 segundos en un minuto, así que voy
to divide by 60.
a dividir entre 60
60 is 10 times 3 times 2.
60 es 10x3x2
That's the way I'm going to do it.
Esta es la forma en la que lo voy a hacer
So I'm going to divide by 60.
Así que voy a dividir entre 60.
I can just cancel out 10 and 3 and 2.
Aquí puedo simplemente eliminar el 10, el 3 y el 2.
That's a way to divide by 60.
Esta es otra forma de dividir entre 60
I might as well cancel out the 1 as well, while I'm at it.
Debería eliminar el 1 también.
How many hours is that?
¿Cuántas horas son eso?
I'm going to divide by 60 again.
Voy a volver a dividir entre 60.
Another way to write 60 is 5 times 4 times 3.
Otra forma de escribir 60 es 5x4x3
That also equals 60.
Eso equivale a 60.
I'm going to cancel out the 5 and the 4.
Ahora voy a eliminar el 5 y el 4.
And I want to cancel 3.
Y también quiero eliminar el 3
I don't have it.
Pero, no tengo,
I'm going to take the 9, divide by 3.
Voy a coger el 9 y lo dividiré por 3
So that now becomes a 3 instead.
Ahora se convierte en un 3
This is how many minutes we've got.
Estos son los minutos que tenemos.
How many hours is that?
¿Cuántas horas son eso?
I want to divide by 24.
Ahora quiero dividirlo por 24
24 is 8 times 3.
24 es 8x3
Divide by 8, and that now disappears.
Divido entre 8, y ahora el 8 desaparece.
Fantastic.
Fantastico.
24 is gone.
Ya hemos dividido entre 24.
So this is how many hours it is.
Estas son las horas.
How many weeks is that?
¿Cuántas semanas son eso?
There are seven days in a week.
Hay 7 días en una semana.
I want to divide by 7.
Así que voy a dividir entre 7.
That's how many weeks it is.
Estas son las semanas de 10! segundos.
How many weeks is it?
¿Cuántas semanas es eso?
What's left?
¿Qué queda?
Six.
Seis
There are exactly six weeks for 10 factorial seconds.
Hay exactamente 6 semanas en 10! segundos.
Exactly.
Exactamente.
So if you're at school, and if you're looking forward to your
Así que si tu estas en la escuela esperando tus
six weeks holiday, and oh, it doesn't seem like long enough,
vacaciones de 6 semanas, y , oh , no te parecen suficiente largas,
well, perhaps you might like to think of it as your 10
bueno, quizá deberías pensar que son tus
factorial second holiday.
vacaciones de 10! segundos.
So let's try this from the other direction.
Vamos a probar esto en la otra dirección.
So how many seconds are there in six weeks?
¿Cuántos segundos hay en 6 semanas?
So we've got six weeks.
Vale, tenemos 6 semanas
How many days is that?
¿Cuántos días son eso ?
How many days are there in six weeks?
¿Cuántos días hay en 6 semanas?
We're going to times by 7.
Lo vamos a multiplicar por 7,
Seven days a week.
ya que una semana tiene 7 días.
How many hours is that?
¿Cuántas horas es eso?
24 hours in a day.
Un día tiene 24 horas,
So we're going to times by 24.
Así que vamos a multiplicar por 24.
How many minutes is that?
¿Cuántos minutos es eso?
Well, let's times by 60.
Bien, multipliquemos por 60
60 minutes in an hour, and then times by 60 again because
porque hay 60 minutos en una hora, y multipliquemos otra vez por 60 porque
there's 60 seconds in a minute.
hay 60 segundos en un minuto.
This is how many seconds you get in six weeks.
Estos son los segundos que hay en 6 semanas
Now we get our calculator.
Ahora cogemos nuestra calculadora,
Let's see if we do get what I said it was going to be.
veamos si va a salir lo mismo que dije.
6 weeks times 7 days times 24 hours times 60 minutes times
(6 semanas) x (7 días) x (24 horas) x (60 minutos) x
60 seconds is exactly what I said before.
(60 segundos) que es exactamente lo mismo que dije antes.
3,628,800, or to put it another way, 10 factorial.
3.628.800, o escrito de otra forma, 10!
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