Question

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

Answer 1

When decimals are multiplied or divided by powers of ten, the decimal point shifts left or right depending on the operation.

1. **Multiplying by Powers of Ten**:
- When you multiply a decimal by a power of ten (like \(10^1, 10^2, 10^3\), etc.), the decimal point moves to the right. The number of places it moves depends on the exponent of the power of ten.
- For example:
- \(2.5 \times 10^1 = 25.0\) (the decimal moves one place to the right)
- \(2.5 \times 10^2 = 250.0\) (the decimal moves two places to the right)
- \(2.5 \times 10^3 = 2500.0\) (the decimal moves three places to the right)

2. **Dividing by Powers of Ten**:
- When you divide a decimal by a power of ten, the decimal point moves to the left. Again, the number of places it moves depends on the exponent of the power of ten.
- For example:
- \(2.5 \div 10^1 = 0.25\) (the decimal moves one place to the left)
- \(2.5 \div 10^2 = 0.025\) (the decimal moves two places to the left)
- \(2.5 \div 10^3 = 0.0025\) (the decimal moves three places to the left)

### Summary:
- **Multiplication by \(10^n\)**: Move the decimal point \(n\) places to the right.
- **Division by \(10^n\)**: Move the decimal point \(n\) places to the left.

This method works for any decimal number and helps in quickly converting between different magnitudes in decimal form.