Quantitative Reasoning : Logarithms

Question

How many zeroes are there between the decimal point and the first significant digit in (1/9)²⁰⁰ given log₁₀3 = 0.4771?

1. 84
2. 85
3. 191
4. 190
   
   

Correct Answer

Choice (4). 190 zeroes

Explanatory Answers

Note:

After taking log to the given number if the mantissa of the logarithm is negative, then the characteristic is equal to the number of zeroes immediately following the decimal point.

Therefore, log (1/9)²⁰⁰ = log (9^-200) = -200 log (3²) = -400 log (3) = -400(0.4771) = -190.84.

Hence, the number (1/9)²⁰⁰ will have 190 zeroes immediately after the decimal point.

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