How many 100-digit positive integers are ther | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$9 	imes 10^{99}$

Vedclass · Answer

(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?

Similar Questions

$989.001 + 1.00982 \times 76.792 = ?$

If $x^{2} + \frac{1}{x^{2}} = 1$,then what is the value of $x^{48} + x^{42} + x^{38} + x^{30} + x^{24} + x^{18} + x^{12} + x^{6} + 1$?

$\frac{1.49 \times 14.9 - 0.51 \times 5.1}{14.9 - 5.1}$

$\frac{3}{5}$ of $\frac{4}{7}$ of $\frac{5}{9}$ of $\frac{21}{24}$ of $504 = ?$

Which of the following are in descending order of their value?

Vedclass Test Series

Exam Paper Generator

Online Exam Module