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