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.
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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).
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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.