How many digits are in the number 50^8 × 8^3 × 11^2?

Question

A. 22
B. 20
C. 19
D. 18
E. 17

chetan2u · Accepted Answer

As we can see 5s and 2s in the term, lets get it in terms of 10s..

50^8 × 8^3 × 11^2 = (5^2)^8*2^8*2^{3*3}*11^2 = 5^{16}*2^{17}*11^2 = 10^{16}*2*121 
so 3 digits from 2*121 and 16 trailing zeroes from  10^{16} ..
total = 3+16 = 19
C

OptimusPrepJanielle · Answer

This might look to be a difficult question on the first glance.
Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10

50^8 × 8^3 × 11^2 = (5^2*2)^8*2^9*11^2 = 5^16*2^17*11^2 = 2*11^2*10^16 = 242*10^16
Hence we would have 16 trailing 0's and the three digits from 242
Total digits = 3 + 16 = 19

Correct Option: C

geeloria · Answer

Hey  Bunuel , could you explain why 16 trailing 0's = 16 digits? Shouldn't it be 17 since the first digit 1 is also include?

Thus 17 + 3 = 20 digits?

Schu20 · Answer

Step 1) Prime Factorization: 50^8 -> (5^2 * 2)^8 = 5^16 * 2^8 | 8^3 -> 2^3*3 = 2^9 | 11^2 
Step 2) Summarize Prime Factorization: -> 5^16 * 2^17 * 11^2 
Step 3) Trailing Zeros: Every 5 & 2 prime factorization accounts for 1 trailing zero, therefore we have  16 Trailing Zeros &  2^1 * 11^2 
Step 4) Solve Remaining digits: 2 * 11^2 = 2*121 = 242 (3 Digits) 
Step 5) Determine Answer: 3 digits + 16 trailing zeros = 19 total digits in this number.

How many digits are in the number 50^8 × 8^3 × 11^2?

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How many digits are in the number 50^8 × 8^3 × 11^2?

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