When multiplying a decimal by a power of 10, the product shifts the decimal point to the right for positive powers of 10 and to the left for negative powers of 10.
- For example, multiplying 0.5 by 10 (which is \(10^1\)) results in 5.0, shifting the decimal one place to the right.
- Conversely, multiplying 0.5 by 0.1 (which is \(10^{-1}\)) results in 0.05, shifting the decimal one place to the left.
In summary, the product shifts the decimal point based on whether the power of 10 is positive (right shift) or negative (left shift).