Determine how many eiphers there are between the decimal point and the first significant digits in ${(\frac{1}{2})}^{100}$ .

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Solution

$x = {(\frac{1}{2})}^{100}$

Taking log on both sides, we get $log x = 100 (log 1 - log 2) = - 103.03$

Hence there are 103 ciphers between the decimal point and the first significant digit

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