To find the value of \( \frac{2\sqrt{a}}{b} \) when \( a = 1.21 \times 10^{-4} \) and \( b = 4.4 \times 10^{-6} \), we will follow these steps:
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Calculate \( \sqrt{a} \): \[ a = 1.21 \times 10^{-4} \] Taking the square root: \[ \sqrt{a} = \sqrt{1.21} \times \sqrt{10^{-4}} = 1.1 \times 10^{-2} \] (since \( \sqrt{1.21} = 1.1 \) and \( \sqrt{10^{-4}} = 10^{-2} \)).
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Calculate \( 2\sqrt{a} \): \[ 2\sqrt{a} = 2 \times 1.1 \times 10^{-2} = 2.2 \times 10^{-2} \]
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Now calculate \( \frac{2\sqrt{a}}{b} \): \[ b = 4.4 \times 10^{-6} \] So, \[ \frac{2\sqrt{a}}{b} = \frac{2.2 \times 10^{-2}}{4.4 \times 10^{-6}} \]
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Divide the coefficients and subtract the exponents: \[ \frac{2.2}{4.4} = 0.5 \] and, \[ 10^{-2} \div 10^{-6} = 10^{-2 - (-6)} = 10^{-2 + 6} = 10^{4} \] Therefore, \[ \frac{2\sqrt{a}}{b} = 0.5 \times 10^{4} \]
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Convert to the form \( A \times 10^n \) where \( A \) is between 1 and 10. To do this: \[ 0.5 \times 10^{4} = 5.0 \times 10^{3} \]
Thus, the final answer is: \[ \boxed{5.0 \times 10^{3}} \]