18. How many digits does the number $2^{100}$ have?
18. The number of digits in the representation of a number is always one more than the characteristic of the decimal logarithm of the number. In our case

$$
\lg 2^{100}=100 \lg 2 \approx 100 \cdot 0.3010=30.10
$$

Therefore, the number $2^{100}$ contains 31 digits.