Question

How do decimals change when multiplied or divided by powers of 10 greater than 1?

Answer 1

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)

### 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)

### 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.