Question

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

Answers

GPT-4o mini
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.

1. **Multiplying 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:
- \( 2.5 \times 10^2 = 2.5 \times 100 = 250 \) (the decimal point moves 2 places to the right).
- \( 0.004 \times 10^3 = 0.004 \times 1000 = 4 \) (the decimal point moves 3 places to the right).

2. **Dividing 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:
- \( 5.6 \div 10^1 = 5.6 \div 10 = 0.56 \) (the decimal point moves 1 place to the left).
- \( 0.75 \div 10^2 = 0.75 \div 100 = 0.0075 \) (the decimal point moves 2 places to the left).

In 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.
can you summerize this
GPT-4o mini
Sure! Here's a summary:

- **Multiplying by powers of 10 (like \( 10^n \))**: Move the decimal point \( n \) places to the **right**.
- Example: \( 2.5 \times 100 = 250 \) (moves 2 places right).

- **Dividing by powers of 10 (like \( 10^n \))**: Move the decimal point \( n \) places to the **left**.
- Example: \( 5.6 \div 10 = 0.56 \) (moves 1 place left).