Question

How do decimals change when multiplied or divided by the power of 10 greater than 1

Answer 1

When you multiply or divide a decimal number by a power of 10 (greater than 1), the position of the decimal point changes. Here's how it works for both multiplication and division:

### Multiplication by Powers of 10
When you multiply a decimal by \(10^n\), where \(n\) is a positive integer, you move the decimal point \(n\) places to the right.

**Example:**
- \(3.45 \times 10^2 = 3.45 \times 100 = 345\) (the decimal moves 2 places to the right).

### Division by Powers of 10
When you divide a decimal by \(10^n\), where \(n\) is a positive integer, you move the decimal point \(n\) places to the left.

**Example:**
- \(5.67 \div 10^2 = 5.67 \div 100 = 0.0567\) (the decimal moves 2 places to the left).

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

This method allows for quick adjustments of decimal values when working with powers of 10.