\( \begin{array}{ll}x=3 & \text { correct to } 1 \text { significant figure. } \\ y=8.37 & \text { correct to } 3 \text { significant figures. } \\ z=5.3 & \text { correct to } 1 \text { decimal place. } \\ \text { Calculate the upper bound of } x(y-z) \\ \text { Show your working clearly. }\end{array} \)

To calculate the upper bound of \( x(y - z) \), we first need to determine the upper bounds of \( x \), \( y \), and \( z \): 1. **For \( x = 3 \) (correct to 1 significant figure)**: The upper bound is found by taking the next half unit above. Hence, the upper bound of \( x \) is: \[ x = 3 + 0.5 = 3.5 \] 2. **For \( y = 8.37 \) (correct to 3 significant figures)**: The upper bound is found by considering the last significant figure. Thus, the upper bound of \( y \) is: \[ y = 8.37 + 0.005 = 8.375 \] 3. **For \( z = 5.3 \) (correct to 1 decimal place)**: The upper bound is determined by adding 0.05 (the next smallest decimal), so the upper bound of \( z \) is: \[ z = 5.3 + 0.05 = 5.35 \] Next, we calculate the upper bound for \( y - z \): \[ y - z = 8.375 - 5.35 = 3.025 \] Now we find the upper bound of \( (y - z) \): \[ \text{Upper Bound of } (y - z) = 8.375 - 5.3 = 3.075 \text{ (using the highest bounds)} \] Finally, we calculate the upper bound of \( x(y - z) \): \[ \text{Upper Bound of } x(y - z) = 3.5 \times 3.075 \] \[ = 10.7625 \] Therefore, the upper bound of \( x(y - z) \) is approximately **10.76** when rounded to three significant figures.