Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What happens to the exponent in scientific notation when the decimal is moved to the right?

1. It increases

2. It stays the same

3. It becomes negative

4. It becomes positive

The correct answer is: It becomes negative

In scientific notation, moving the decimal point to the right results in the exponent decreasing. This is because moving the decimal to the right indicates the number is becoming smaller, and you adjust the exponent accordingly to reflect this change in magnitude. Therefore, when you shift the decimal right, you are essentially dividing by 10 for each place you move it, thus the exponent becomes negative to indicate this reduction in size. For instance, if we were expressing 3000 in scientific notation, moving the decimal point from the end of the number to after the first non-zero digit results in the expression of the number as \(3.0 \times 10^3\). If we were to move the decimal point to create a smaller number like 30, we would represent that as \(3.0 \times 10^1\). As you can see, shifting the decimal consistently affects the exponent in a way that it will be negative when we account for the decimal moving to the right. This concept is essential in understanding how to properly convert between standard number formats and scientific notation.