# How many digits are in the decimal representation of $\frac{2^{2001}5^{1950}}{4^{27}}$?

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.