To subtract the two scientific numbers \( 8.03 \times 10^{-8} \) and \( 2.56 \times 10^{-2} \), we need to express both numbers with the same power of ten.
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Convert \( 2.56 \times 10^{-2} \) to a compatible power of ten:
We can express \( 2.56 \times 10^{-2} \) in terms of \( 10^{-8} \):\[ 2.56 \times 10^{-2} = 2.56 \times 10^{6} \times 10^{-8} = 25.6 \times 10^{-8} \]
(Here, we moved the decimal point 6 places to the right, which is expressed as \( 10^{6} \), effectively reducing the exponent from \(-2\) to \(-8\)).
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Now we can subtract:
\[ 8.03 \times 10^{-8} - 25.6 \times 10^{-8} = (8.03 - 25.6) \times 10^{-8} \]
\[ = -17.57 \times 10^{-8} \]
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Express the answer in proper scientific notation:
To express \(-17.57 \times 10^{-8}\) in proper scientific notation, we need the coefficient to be between 1 and 10. We can rewrite it as:\[ -1.757 \times 10^{-7} \]
(We moved the decimal point one place to the left, which increases the exponent by 1).
Thus, the final answer for the subtraction is:
\[ \boxed{-1.757 \times 10^{-7}} \]
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