What is the Sum of Digits for 2^1000?

In summary, the conversation discusses finding the sum of the digits of 2^1000 and the issue with equating 2^1000 to 10^301. It is suggested to look at the series of numbers to solve the problem and to work modulo 9 to get the single digit reduced sum. The final answer is 7.
  • #1
Krypton
13
0
What is the sum of the digits of 2^1000
check my algoriathm, let y=2^1000 then logy = 1000log2 = 301 and y=10^logy=10^301
since (1,0) r da only digits of 10^n 4all n=1,2,3,4,... The sum of digits equals 1 , but it is not the answer ...Why?
 
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  • #2
Well you seem to want 2^1000 to be equal to 10^301 which is clearly false since 5 divides the latter but not the former. The issue is that 1000log2 is not exactly equal to 301, you probably left off the decimal places which is the cause of your problem when you equate 10^logy to 2^1000.
 
  • #3
That 301 is just the number of zeros, since log(2) = .301029996...you are attempting to approximate its value using 1000log(2) = 301.

However the problem can be worked out by looking at the series, 2, 4, 8, 16=7, 32=5, etc.
 
  • #4
Hay i am not using a computer to calculate it that way. I need some techiques could u pleasezzzz...Z
 
  • #5
Do you want the actual sum of all the digits in 2^1000 or do you just want the single digit reduced sum (the single digit eventually obtained from repeated summing of digits).

If its the single digit reduced sum that you want then just work modulo 9 to get the answer (which is 7 btw).
 

1. What is the sum of digits for 2^1000?

The sum of digits for 2^1000 is 1366.

2. How do you calculate the sum of digits for 2^1000?

The sum of digits for 2^1000 can be calculated by first finding the value of 2^1000, which is a very large number. Then, add together all the individual digits in the number to get the sum.

3. Is there a shortcut or formula for finding the sum of digits for 2^1000?

There is no specific formula for finding the sum of digits for 2^1000, but it can be calculated using basic addition and the knowledge of powers of two.

4. Why is the sum of digits for 2^1000 important?

The sum of digits for 2^1000 may not have a specific significance, but it can be used as a mathematical exercise and can also be helpful in understanding the properties of large numbers and powers.

5. Can the sum of digits for 2^1000 be calculated for other powers of two?

Yes, the sum of digits for any power of two can be calculated using the same process as for 2^1000. However, the sum will vary depending on the power of two being used.

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