To find the thickness of a fingernail given the diameter of a human hair and the additional thickness, we start by converting the diameter of the hair from scientific notation to decimal form.
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The diameter of the hair is \(4 \times 10^{-8}\) inches. In decimal form, this is:
\[ 4 \times 10^{-8} = 0.00000004 \text{ inches} \]
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The thickness of the fingernail is given as \(0.011\) inches thicker than the diameter of the hair. We can express this with the following addition:
\[ \text{Thickness of fingernail} = 0.011 + (4 \times 10^{-8}) \]
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Since \(4 \times 10^{-8} = 0.00000004\) is very small compared to \(0.011\), we can add these two numbers directly, with \(0.011\) being the dominant figure. We can format \(0.011\) to a common decimal place for easier addition:
\[ 0.011 = 0.01100000 \]
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Now add:
\[ 0.01100000 + 0.00000004 = 0.01100004 \]
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To express the answer correctly to three decimal places, we round the result:
\[ 0.01100004 \approx 0.011 \]
So, the thickness of the fingernail, when rounded to three decimal places, is:
\[ \boxed{0.011} \] inches.
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