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.


$\frac{10^{1950}}{8} = 10^{1947} \times \frac{1000}{8} = 125 \times 10^{1947}$, 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.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.