When multiplying a decimal by a power of 10, the product is obtained by shifting the decimal point to the right. Each time you multiply by 10, you move the decimal point one place to the right. For example:
- \( 2.5 \times 10^1 = 25.0 \) (shift one place right)
- \( 2.5 \times 10^2 = 250.0 \) (shift two places right)
When dividing a decimal by a power of 10, the quotient is obtained by shifting the decimal point to the left. Each time you divide by 10, you move the decimal point one place to the left. For example:
- \( 2.5 \div 10^1 = 0.25 \) (shift one place left)
- \( 2.5 \div 10^2 = 0.025 \) (shift two places left)
In summary:
- Multiplying by 10: Shift the decimal point to the right.
- Dividing by 10: Shift the decimal point to the left.