The number of digits in the number N=2^12 5^8 is

N=2^125^8=2^42^85^8=2^4(25)^8=2^410^8=16100000000, which has 2+8=10 digits, so the answer is 10.

smc

number theory intermediate

Problem

The number of digits in the number

N = 2^{12} \times 5^{8}

(A)

9

(B)

10

(C)

11

(D)

12

Solution

N = 2^{12} \cdot 5^{8} = 2^{4} \cdot 2^{8} \cdot 5^{8} = 2^{4} \cdot (2 \cdot 5)^{8} = 2^{4} \cdot 1 0^{8} = 16 \cdot 100000000

, which has

2 + 8 = 10

digits, so the answer is

10

Final answer