How many 100-digit positive integers are ther | vedclass

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(A) To find the number of $n$-digit positive integers,we consider the range of numbers.For a $100$-digit number,the smallest number is $1$ followed by

Vedclass · Accepted Answer

$9 	imes 10^{99}$

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(A) To find the number of $n$-digit positive integers,we consider the range of numbers.For a $100$-digit number,the smallest number is $1$ followed by $99$ zeros,which is $10^{99}$.The largest $100$-digit number is $10^{100} - 1$ (which consists of $100$ nines).The total count of such numbers is given by the formula: $(	ext{Largest } n	ext{-digit number}) - (	ext{Smallest } n	ext{-digit number}) + 1$.Substituting $n = 100$:Total count $= (10^{100} - 1) - (10^{99}) + 1$.Total count $= 10^{100} - 10^{99}$.Factoring out $10^{99}$:Total count $= 10^{99} 	imes (10 - 1) = 9 	imes 10^{99}$.

How many $100$-digit positive integers are there?

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