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Sum of digits?

The sum of digits of the number \(2^{2000}\times 5^{2004}\)?

I am not getting to even solve such problems. Please put some of the general methods and example if possible with their proper solutions.

Note by Puneet Pinku
3 months ago

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Hi well i m not sure that my answer is correct (as i m in class9) according to me solution is

2^2000 × 5^2004 =2^2000×5^2000 × 5^4 =(2^2000×5^2000) + 25×25 ... '+' sign for sum of digits

=10^2000 × 625

Sum of digits = 626 Mafia MaNiAc · 3 months ago

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@Mafia MaNiAc CORRECTION : ...... = 2^2000×5^2000×5^4 =10^2000 × 625 THEREFORE DIGIT SUM = 6+2+5 =13 ..... Q.E.D. Mafia MaNiAc · 3 months ago

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Comment deleted 1 month ago

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@Puneet Pinku I know this is 5 weeks ago, but the one that comes from the \(10^{2000}\) isn't actually in the final product.

If we reduce the exponent to numbers that are easier to handle, this becomes more evident. Lets do \(10^{0}\).

\(10^{0} \times 625=625\), so the digit sum is \(6+2+5=13\)

Adding another \(10\), \(10^{1} \times 625 = 6250\), and the digit sum is still \(13\).

By adding another factor of 10 we are really just adding another 0 to the end of our previous number, which does not affect the digit sum Brandon Monsen · 1 month, 2 weeks ago

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@Brandon Monsen Ya! You are, even I was surprised that before asking Mafia Maniac to correct his solution I myself was wrong. Thanks!!! Puneet Pinku · 1 month, 2 weeks ago

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@Puneet Pinku Can u pls tell me how do u add "image" while giving question/problem? Mafia MaNiAc · 3 months ago

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@Mafia MaNiAc

Whenever you post a problem use this tool to select and add images from your computer.

Whenever you post a problem use this tool to select and add images from your computer.

Tapas Mazumdar · 1 month, 2 weeks ago

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