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Let M be the number of digits in 11⁵⁰ and N be the number of zeros after the decimal point but before the first significant digit in (0.11)⁵⁰. Given that log10(11) = 1.041, identify the correct statement(s).

1. M = 52
2. M = 53
3. N = 47

Correct answer: M = 53

Solution

log10(11⁵⁰) = 52.05, so M = 52+1 = 53. log10(0.11⁵⁰) = -47.95 = -48 + 0.05, meaning the number is 10^(-48)*10^(0.05), which has 47 zeros after the decimal point before the first significant digit, so N = 47.

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