Question

how many times does the digit 1 appear when you write numbers 1 to 399 consecutively​

Answer 1

Answer:

May be 16 cause 1,11,21,31,41,51,61,71,81,91,100,121,131,

Answer 2

ANSWER:

1 appears 180 times when you write numbers 1 to 399 consecutively

SOLUTION:

Let's consider the values from 000 to 399  

NOTE: Yes, I have started at 000 and ended at 399, even though the question asks us to look at the numbers from 1 to 399.  

HOWEVER, notice that 000 and 399 do not have any 1's so the outcome will be the same.  

Okay, there are 400 integers from 000 to 399  

UNITS position  

Each of the 10 digits (0, 1, 2, 3..., 9) appears the same number of times in the UNITS position.  

So, the digit 1 must occur 1/10 of the time in this position.  

So, the digit 1 must appear (1/10)(400) times, which equals 40 times.  

TENS position  

Each of the 10 digits (0, 1, 2, 3..., 9) appears the same number of times in the TENS position.  

So, the digit 1 must occur 1/10 of the time in this position.  

So, the digit 1 must appear (1/10)(400) times, which equals 40 times.  

HUNDREDS position  

The 1 appears in the HUNDREDS position in every integer from 100 to 199  

So, the digit 1 appears 100 times.  

Now, TOTAL = 40 + 40 + 100 = 180.

Hence, 1 appears 180 times.