To divide the numbers in scientific notation \((2 \times 10^{10})\) by \((8 \times 10^{3})\), you can follow these steps:
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Divide the coefficients (the numbers in front): \[ \frac{2}{8} = 0.25 \]
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Subtract the exponents of 10: \[ 10^{10 - 3} = 10^{7} \]
Now combine the results: \[ 0.25 \times 10^{7} \]
To express this in standard scientific notation, we need the coefficient to be between 1 and 10. We can rewrite \(0.25\) as \(2.5 \times 10^{-1}\):
\[ 0.25 \times 10^{7} = (2.5 \times 10^{-1}) \times 10^{7} \]
Now, combine the powers of 10: \[ 2.5 \times 10^{7 - 1} = 2.5 \times 10^{6} \]
Thus, the final result in scientific notation is: \[ \boxed{2.5 \times 10^{6}} \]