To perform the addition \( 4.21 \times 10^{-5} + 219.11 \), we need to express both numbers in the same format, preferably as decimal numbers for easier addition.
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Convert \( 4.21 \times 10^{-5} \) to decimal: \[ 4.21 \times 10^{-5} = 0.0000421 \]
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Now add \( 0.0000421 \) and \( 219.11 \): \[ 219.11 + 0.0000421 \approx 219.11 \] (Since \( 0.0000421 \) is a very small number compared to 219.11, it will not significantly change the result).
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Performing the exact addition:
- Align the numbers for addition: \[ \begin{array}{r} 219.1100000 \
- 0.0000421 \ \hline 219.1100421 \ \end{array} \]
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Thus, the final result is: \[ 4.21 \times 10^{-5} + 219.11 = 219.1100421 \]
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For reporting purposes, you might round this based on significant figures. However, since the first number contributes very little in terms of significant digits, the final answer could simply be: \[ 219.11 \]
Hence, the precise result is \( \mathbf{219.1100421} \) but depending on context, it may be simplified to \( \mathbf{219.11} \).