Consider: a=3.2pm 0.5 b=1.5pm 0.1 c=6.07pm 0.09 What is the uncertainty in a+(c)/(b) 7

Here's how to calculate the uncertainty in $a + \frac{c}{b}$:<br /><br />1. **Calculate the value of the expression:**<br /><br /> $a + \frac{c}{b} = 3.2 + \frac{6.07}{1.5} = 3.2 + 4.0467 \approx 7.2467$<br /><br />2. **Calculate the fractional uncertainty of $\frac{c}{b}$:**<br /><br /> Fractional uncertainty in *c* = $\frac{0.09}{6.07} \approx 0.0148$<br /> Fractional uncertainty in *b* = $\frac{0.1}{1.5} \approx 0.0667$<br /> Fractional uncertainty in $\frac{c}{b}$ = Fractional uncertainty in *c* + Fractional uncertainty in *b* <br /> = $0.0148 + 0.0667 \approx 0.0815$<br /><br />3. **Calculate the absolute uncertainty of $\frac{c}{b}$:**<br /><br /> Absolute uncertainty in $\frac{c}{b}$ = Fractional uncertainty in $\frac{c}{b}$ * Value of $\frac{c}{b}$<br /> = $0.0815 * 4.0467 \approx 0.330$<br /><br />4. **Calculate the absolute uncertainty of $a + \frac{c}{b}$:**<br /><br /> Since *a* and $\frac{c}{b}$ are added, we add their absolute uncertainties:<br /><br /> Absolute uncertainty in $a + \frac{c}{b}$ = Absolute uncertainty in *a* + Absolute uncertainty in $\frac{c}{b}$<br /> = $0.5 + 0.330 = 0.830$<br /><br />5. **Final Result:**<br /><br /> $a + \frac{c}{b} = 7.2 \pm 0.8$ (We round the final value to one significant figure in the uncertainty and align the decimal place in the value accordingly.)<br /><br />Therefore, the uncertainty in $a + \frac{c}{b}$ is approximately 0.8.<br />