How many times digit 1 appear in the page numbers of a book?

A book has 500 pages numbered 1,2,3 and so on. How many times does the digit 1 appear in the page numbers?

Units Place:
Digit 1 occurs in unit place once in every 10 numbers. i.e; 1, 11, 21, 31, ...... 491
We have 50 ten number groups till 500.
i.e; Digit 1 occurs 50 times in units place.

Tens Place:
Digit 1 occurs in tens place 10 times in every 100 numbers.i.e; 110,111,112, .... , 210, 211,.... 419.
We have 5 hundred number group till 500.
i.e; Digit 1 occurs 50 times in tens place.

Hundreds Place:
Digit 1 occurs 100 times from 100 to 199 in hundreds place till 500.

So digit '1' appears 200 times from 1,2,3 ... till 500