Stupid Question (1 Viewer)

[ayehann]

Hey guys.. sorry ive completely forgotten how to do this. its from a past hsc...

if 2^10 = 1024, and has 4 digits... how many digits does 2^1000 have??

 

[kooltrainer]

it shuld give u math error.. so 0 digits..

 

[Aquawhite]

One mother of a number

 

[ayehann]

BTW the answe is 302 digits. but how do we figure it out

 

[chris1515]

I went over this same question with my tutor. It's the second part isn't it. My tutor who is also a maths teacher said do not worry about it for the 2 unit paper. He said there was controversy about it not even being in the course. So i guess just leave it. If you do want the answer i can find it for you

 

[ayehann]

It's the second part isn't it.

yep

 

[chris1515]

Wouldnt bother then

 

[Drongoski]

Wouldnt bother then

Maybe yr tutor found it hard also. I've been giving it a thought and maybe this is how you figure it out.

The number of digits is given by log₁₀ 2¹⁰⁰⁰

= log₂ 2¹⁰⁰⁰ / log₂ 10

= 1000 x log₁₀ 2 = 1000 x 0.30102999 .. = 301.029 ...

= 302 ( nearest whole number)

= the number of decimal digits.

PS: log₂ 10 = log₁₀ 10 / log₁₀ 2 = 1/ log₁₀ 2 (change of base)

This ought to be a 3U question; I'm sure most 4U students would find it hard.

 

[chris1515]

Maybe yr tutor found it hard also. I've been giving it a thought and maybe this is how you figure it out.

The number of digits is given by log₁₀ 2¹⁰⁰⁰

= log₂ 2¹⁰⁰⁰ / log₂ 10

= 1000 x log₁₀ 2 = 1000 x 0.30102999 .. = 301.029 ...

= 302 ( nearest whole number)

= the number of decimal digits.

PS: log₂ 10 = log₁₀ 10 / log₁₀ 2 = 1/ log₁₀ 2 (change of base)

This ought to be a 3U question; I'm sure most 4U students would find it hard.

Nah my tutor could do it, he's a teacher and marked it in the hsc that it was found in. Its not relevant cause it's not in the 2 unit course. But yeah your right it could be found in the 3 or 4 unit tests. And 302 is the right answer.

 

[m.jakaran]

This is quite an interesting question and originally came in one of those AMC competitions, like around Q13 so its not meant to be that hard. Just express 2^1000 and 10^something and then you know that 10^1 has 2 digits, 10^2 has 3 and so on.

 

[m.jakaran]

2^1000 =10^301.029

and 10^n has n+1 digits

hence there are 302 digits

 

[Drongoski]

2^1000 =10^301.029

and 10^n has n+1 digits

hence there are 302 digits

Interesting and easy-to-understand; good work.

 

[Top Secret]

2^1000 =10^301.029

and 10^n has n+1 digits

hence there are 302 digits

Very nice...

 

[cutemouse]

I recall seeing this... Is it from the 2001 HSC? (CBF looking it up now)