When multiplying a decimal by a power of 10, the product is obtained by moving the decimal point to the right for positive powers of 10 or to the left for negative powers of 10.
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For positive powers of 10 (e.g., 10^1, 10^2, etc.), the decimal point moves to the right:
- Example: \( 2.5 \times 10^2 = 2.5 \times 100 = 250 \) (the decimal point moves 2 places to the right)
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For negative powers of 10 (e.g., 10^-1, 10^-2, etc.), the decimal point moves to the left:
- Example: \( 2.5 \times 10^{-2} = 2.5 \times 0.01 = 0.025 \) (the decimal point moves 2 places to the left)
This allows for a simple way to scale decimal numbers up or down by factors of ten.