Quick Question (1 Viewer)

[Ali92l]

The success one answer don't make much sense to me.

b) i Find log(Base 10) 2^1000 correct to 3. d.p
ii We know that 2^10 = 1024. so that 2^10 can be represented by a 4 digit numeral. How many digits are there in 2^1000 when written as a numeral?



Part i is pretty simple, answer comes out to be 303.03. I can't grasp the concept of ii though, and the crappiest part about that is... its only 1 mark

 

[lyounamu]

The success one answer don't make much sense to me.

b) i Find log(Base 10) 2^1000 correct to 3. d.p
ii We know that 2^10 = 1024. so that 2^10 can be represented by a 4 digit numeral. How many digits are there in 2^1000 when written as a numeral?



Part i is pretty simple, answer comes out to be 303.03. I can't grasp the concept of ii though, and the crappiest part about that is... its only 1 mark

i) log (base 10) 2^1000 = 1000 log(base 10) . 2 = 301.0299957... = 301.030

It's actually 301.030 not 303.03

ii) Refer back to (i)
So if you use the same format here:
log (base 10) 2^10 = 3.010299957 = so there are 4 digits all together because if you think about it 10^3.010299957... has 4 digits all together.
log (base 10) 2^100 = 301.03... = so there are 302 digits all together because 10^301.03... has 302 digits all together.

EDIT: Hope my working out explained itself.

 

[lolokay]

log₁₀2¹⁰⁰⁰ = 301.03

so 10^301.03 = 2¹⁰⁰⁰
what ever the power of 10 is, the number of digits of the number is 1 more than that (rounded down), so the number of digits is 302

 

[Ali92l]

303.03 Must've been a transcription error :S .

Thankyou for the help, Much appreciated.