Consider: a=3.2pm 0.5 b=1.5pm 0.1 c=6.07pm 0.09 What is the uncertainty in 2(ab)/(c)

Here's how to calculate the uncertainty in $2\frac{ab}{c}$:<br /><br />1. **Calculate the value of the expression:**<br /><br /> $2\frac{ab}{c} = 2 \times \frac{3.2 \times 1.5}{6.07} \approx 1.58$<br /><br />2. **Find the fractional uncertainty of each variable:**<br /><br /> * $\frac{\delta a}{a} = \frac{0.5}{3.2} = 0.15625$<br /> * $\frac{\delta b}{b} = \frac{0.1}{1.5} = 0.06667$<br /> * $\frac{\delta c}{c} = \frac{0.09}{6.07} = 0.01483$<br /><br />3. **Calculate the fractional uncertainty of the expression:** When multiplying and dividing, we add the fractional uncertainties:<br /><br /> $\frac{\delta (2ab/c)}{2ab/c} = \frac{\delta a}{a} + \frac{\delta b}{b} + \frac{\delta c}{c} = 0.15625 + 0.06667 + 0.01483 = 0.23775$<br /><br />4. **Calculate the absolute uncertainty of the expression:**<br /><br /> $\delta (2ab/c) = \frac{2ab}{c} \times \frac{\delta (2ab/c)}{2ab/c} = 1.58 \times 0.23775 \approx 0.38$<br /><br />Therefore, the final answer is $1.58 \pm 0.38$.<br />