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My answer is 1950, but the answer sheet says 1949. I think the answer sheet is wrong.

How many digits are in the value of the following expression: $(2^{2001}*5^{1950})/4^{27}$?

I solve this problem as following: $(2^{2001}*5^{1950})/4^{27}=(2*5)^{1950}*2^{51}/2^{54}=10^{1950}/8$, which give total digits of 1950.

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$\frac{10^{1950}}{8} = 10^{1947} \times \frac{1000}{8} = 125 \times 10^{1947}$, which is $125$ followed by $1947$ zeros, hence has $1950$ digits.

However, if we divide by $2$ only then would the answer would drop to $1949$ digits. So I think there is a mistake in the answer sheet. You are correct.

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  • $\begingroup$ One more bug (or al least typo) in a textbook ! $\endgroup$ – Claude Leibovici Oct 27 '16 at 6:25
  • $\begingroup$ @ClaudeLeibovici You should read Indian textbooks. They are the most uncompromising,especially M.L Khanna, Viraf Dalal etc. Only the cookery books are well written. $\endgroup$ – астон вілла олоф мэллбэрг Oct 27 '16 at 10:57
  • $\begingroup$ Is there any one I could read online ? Curious to see (if you give me a link). Thanks. $\endgroup$ – Claude Leibovici Oct 27 '16 at 10:59
  • $\begingroup$ @ClaudeLeibovici I actually do not know how many of them are online. I have hard copies of all the above. An ordinary search doesn't throw up the books I would have wanted you to read. Though, Sunita Arora could be online... no I can't find it immediately. I'll get back if I can find you some book. Though you will never thank me after reading it. $\endgroup$ – астон вілла олоф мэллбэрг Oct 27 '16 at 11:02

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