Question

How many times does the digit 1 appear in numbers from \[1\] to \[100\]?
A. \[18\]
B. \[19\]
C. \[20\]
D. \[21\]

Answer 1

Hint: We will count the digit 1 in a range of 10 numbers like from 1-10, 11-20, and so on.
Here, in the number 11, 1 appears twice and in the range 11-20 it will appear many times.
At last, we will add the times and we will get the final answer.

Complete step-by-step solution:
We have to find the number of times the digit 1 appears in numbers from \[1\] to \[100\].
From \[1\] to \[10\], 1 the digit 1 appears two times for 1 and 10.
From \[11\] to \[20\], 1 the digit 1 appears in 11, 12, 13, 14, 15, 16, 17, 18, 19 and in 11 it appears twice. So, it appears ten times.
From \[21\] to \[30\], 1 the digit 1 appears only once for 21.
From \[31\] to \[40\], 1 the digit 1 appears only once for 31.
From \[41\] to \[50\], 1 the digit 1 appears only once for 41.
From \[51\] to \[60\], 1 the digit 1 appears only once for 51.
From \[61\] to \[70\], 1 the digit 1 appears only once for 61.
From \[71\] to \[80\], 1 the digit 1 appears only once for 71.
From \[81\] to \[90\], 1 the digit 1 appears only once for 81.
From \[91\] to \[100\], 1 the digit 1 appears two times for 91 and 100.
So, the total number of times of repetition of 1 is \[2 + 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 = 21\]
Hence, the digit 1 appears in numbers from \[1\] to \[100\] for 21 times.

Hence, the correct answer is D.

Note: The counting of a specific digit in a given range of numbers can be done by determining the count of digits on a specific position of the numbers in the smaller range and then multiplying it to get the digit in the position for a larger range.
This can be repeated for all the positions of the numbers in the given range.