The shortcut is to remember that when you are multiplying by 10, 100, 1000, or 10000,... you move the decimal place in the number you are multiplying TO THE RIGHT (i.e., make the number BIGGER) by the number of zeros you see in the 10, 100, 1000, 10000,...
That is readily seen: 4 x 10 = 40
Originally the decimal point was after the 4. (If the decimal point is not shown, it is at the end of the number.) Now its moved over 1 place to make 40, because you are multiplying by 10 which has 1 zero. One zero means move the decimal one place.
4 x 100 = 400. See that the decimal point, originally after the 4 is now over 2 places, because you are multiplying by 100 which has 2 zeros, to make 400.
So in your problem the decimal point is in between the first two zeros. You are multiplying by 1000. That has 3 zeros. So the decimal point is moved 3 place to make the number bigger, so move it to the right. You have to ADD a zero to make that happen. You can't leave an empty space in a number. You must fill in with zeros for the number "to reach" the decimal point. So, 0.03 x 1000 = 0030. which equals 30.
Casey likely started from the beginning of the written number and counted over 3 places, and then planted the decimal, which would put it behind the 3. But Casey should have starting from where the decimal point actually is, and then count over 3 places, which out the decimal one place PAST the 3. As previously stated, you can't leave an empty space in a number. You must fill in with zeros for the number "to reach" the decimal point. That makes the answer 30.
