Hello, sundance240!

How many digits does the number 2^100 have?

Using complicated caculator softwares, it has 31 digits,

but how will you find out with pencil and paper?

We note that: .2^{10} .= .1024 .≈ .10^3

Hence: .2^{100} .≈ .(10^3)^{10} .= .10^{30}

. . which has 31 digits.