To solve the expression \(32.8 + (8.03 \times 10^{-8})\), we need to ensure both numbers are in a comparable format, preferably expressed in scientific notation.
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Convert 32.8 to scientific notation: \[ 32.8 = 3.28 \times 10^1 \]
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Keep \(8.03 \times 10^{-8}\) as it is.
Now we have: \[ 3.28 \times 10^1 + 8.03 \times 10^{-8} \]
Since \(10^1\) (which equals 10) is much larger than \(10^{-8}\), we can approximate the sum without the second term initially. To add these two terms accurately, we need to express \(3.28 \times 10^1\) in terms of \(10^{-8}\): \[ 3.28 \times 10^1 = 3.28 \times 10^1 \times 10^{-8} \times 10^8 = 3.28 \times 10^9 \times 10^{-8} = 32.8 \times 10^1 = 32.8 \times 10^9 \times 10^{-8} \]
Now we rewrite \(3.28 \times 10^1\) in terms of \(10^{-8}\): \[ 3.28 \times 10^1 = 3.28 \times 10^9 \times 10^{-8} = 32.8 \times 10^{-8} \]
Next, we can add: \[ 32.8 \times 10^{-8} + 8.03 \times 10^{-8} = (32.8 + 8.03) \times 10^{-8} = 40.83 \times 10^{-8} \]
- Convert back to scientific notation: \[ 40.83 \times 10^{-8} = 4.083 \times 10^{-7} \]
Looking at the answer choices you provided:
A. \(8000000803 \times 10^2\)
B. \(3.2000000803 \times 10^1\)
C. \(8.03 \times 10^2\)
D. \(80.3 \times 10^3\)
None matches our result \(4.083 \times 10^{-7}\). It appears these choices may not directly represent the correct result from the problem or some error might occurred in the transcription of choices or in problem itself.
To summarize, the correct answer in scientific notation for the problem is: \[ 4.083 \times 10^{-7} \]