1410.11 – How Many Digits?


How many digits are there in the number N =213 59N = 2^{13} · 5^9?


Solution

N =213 59 =24 29 59 =24 109 =16109 =1.61010,N = 2^{13} · 5^9 = 2^4 · 2^9 · 5^9 = 2^4 · 10^9 = 16 · 10^9 = 1.6 \cdot 10^{10}, which has 1111 digits.