SOLUTION: Which of these is closest to the number of digits in the number {{{ 2^1000 }}} when it is written out in full with no indices? A. 100 B. 300 C. 500 D. 1000

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Which of these is closest to the number of digits in the number {{{ 2^1000 }}} when it is written out in full with no indices? A. 100 B. 300 C. 500 D. 1000      Log On

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Question 984002: Which of these is closest to the number of digits in the number +2%5E1000+ when it is written out in full with no indices?
A. 100
B. 300
C. 500
D. 1000
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
We find its logarithm base 10, which we have access to on most every calculator,
whether graphing or only scientific.

log%2810%2C2%5E1000%29=+1000log%2810%2C2%29+=+1000%280.3010299957%29+=+301.02999566398

That means that 21000 is approximately equal to 10301.0299957

Then 10301.02999566398 = 10301100.02999566398 = 10301(1.0715086071833) = 

1.0715086071833 × 10301.

That's the scientific notation for 21000
If we moved the decimal 301 places to the right the number would have 302
digits.

Edwin