Moving Decimal Point in 512.415: Finding the Thousandths Position

How many places to the left should the decimal point be moved in the number 512.415 in order that the 4 becomes the thousandths digit?

To solve this problem, we need to reposition the decimal point such that the digit '4' becomes the thousandths digit.

Currently, the number is 512.415. Let's analyze what each digit represents:

• The '5' is in the hundreds place.
• The '1' is in the tens place.
• The '2' is in the ones place.
• The '4' is in the tenths place.
• The '1' is in the hundredths place.
• The '5' is in the thousandths place.

The digit '4' is initially in the tenths place. We want to move it to the thousandths place.

To make '4' the thousandths digit, consider the placement relative to the decimal point. The decimal place values are as follows: tenths ($10^{-1}$), hundredths ($10^{-2}$), thousandths ($10^{-3}$).

Currently, '4' is at the tenths position. By moving the decimal point two places to the left, '4' will become the thousandths digit. The new number arrangement is $5.12415$.

Thus, the decimal point must be moved 2 places to the left.

The correct answer is $\boxed{2}$.