To determine what we should multiply the coefficient (0.0045) by in order to turn it into a number between 1 and 10, let's follow these steps:
1. Understand the goal: We need to convert 0.0045 to a number within the range of 1 to 10.
2. Move the decimal point: To do this, we will move the decimal point to the right until the number falls within the desired range.
3. Identify the multiplier:
- When we move the decimal point one place to the right, 0.0045 becomes 0.045. This is still not within the range of 1 to 10.
- Moving it two places to the right, 0.0045 becomes 0.45, which is also not within the range of 1 to 10.
- Moving it three places to the right, 0.0045 becomes 4.5, which is indeed within the range of 1 to 10.
4. Determine the corresponding power of 10: Each move of the decimal point to the right corresponds to multiplying by 10 raised to the power of the number of moves. So, moving it three places to the right means multiplying by [tex]\(10^3\)[/tex].
Therefore, to convert 0.0045 to a number between 1 and 10, we should multiply it by [tex]\(10^3\)[/tex] (which is 1000). This transforms 0.0045 into 4.5. The correct answer is to multiply by [tex]\(10^3\)[/tex] (move the decimal by three places).
