Number of times is the digit 5 written when listing all numbers from 1 to 10^5?

Question

Accepted Answer

Correct answer: 50000. (50000) We have to count the occurrences of digit 5 consider integers t such that 0 ≤ t ≤ 10^5 The largest number t having 5 in the units place is 99995.So there are 1 + 9999 = 104 numbers t having 5 in the units place The are 5, 15, 25,............99995 We can describe these numbers as t = x ^5 Where x is any one of 0, 1, 2,......9999. Similarly numbers t = x5y. ie.e., numbers having 5 in the ten's place are in all (1 + 999) × 10 = 104 as x can be any one of 0, 1, 2,..999 and y can be anyone of 0, 1,2,.......9 In the same way, there are 104 numbers in each of the following cases: numbers with 5 in the hundreds place or thousands place or ten thousands place. Hence, the total number of times 5 is written 104 × 5

$Number of times is the digit 5 written when listing all numbers from 1 to 1 0^{5} ?$

Solution

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