When you multiply or divide a decimal by powers of 10 (like 10, 100, 1000, etc.), the decimal point moves to the right or left, respectively.
Multiplying by Powers of 10
- When you multiply a decimal by a power of 10, you move the decimal point to the right. The number of places you move it corresponds to the exponent of the power of 10.
- For example:
- \( 2.5 \times 10^1 = 25.0 \) (move the decimal one place to the right)
- \( 3.75 \times 10^2 = 375.0 \) (move the decimal two places to the right)
- \( 0.47 \times 10^3 = 470.0 \) (move the decimal three places to the right)
- For example:
Dividing by Powers of 10
- When you divide a decimal by a power of 10, you move the decimal point to the left. Again, the number of places you move it corresponds to the exponent of the power of 10.
- For example:
- \( 6.4 \div 10^1 = 0.64 \) (move the decimal one place to the left)
- \( 5.92 \div 10^2 = 0.0592 \) (move the decimal two places to the left)
- \( 1.25 \div 10^3 = 0.00125 \) (move the decimal three places to the left)
- For example:
Summary
- Multiplication by \( 10^n \) (n > 0): Move the decimal point n places to the right.
- Division by \( 10^n \) (n > 0): Move the decimal point n places to the left.
This manipulation helps to adjust the scale of the numbers while preserving their value.