I'm learning College Algebra myself. I have a topic as the following: The set, S consists of 900,000,000 whole numbers, each being the same number of digits long. How many digits long is a number from S? (Hint: use the fact that a whole number cannot start with the digit 0.)
But I don't really understand "each being the same number of digits long". May anyone help me explain this part? I'll find the answer myself then. Thanks a lot!
First off, if you copied the question to the letter, it is a bad question. Did you change the phrasing or leave anything out?
Let's do a bit of a smaller example. Suppose that the number was 90 rather than 900,000,000. Then you will note that the 90 numbers $$ 10, 11, 12, 13, 14, 15, \ldots, 97, 98, 99 $$ all have exactly 2 digits. So if your set consists of these 90 numbers, then the correct answer is 2. This is also presumably the intended answer to the question (at least if you replace 900,000,000 with 90).
(Note that the numbers "$01, 02, 03, \ldots, 09$" don't count: for the purposes of this question, numbers do not have leading zeroes, so these numbers should be written "$1, 2, 3, \ldots, 9$" and therefore have 1 digit, not 2.)
However, the 90 numbers $$ 110, 111, 112, \ldots, 197, 198, 199 $$ all have exactly 3 digits. So your set could consist of these 90 numbers as well, and then the answer would be 3. Because the question (as you wrote it) doesn't specify that the set $S$ should contain all numbers with that number of digits. If you add that condition, then the answer to the modified question is unequivocally 2.
Can you do the question for the number 900,000,000 (instead of 90) yourself?