Bounds Subtraction 43Ad3A

1. **State the problem:**\nWe have two numbers $c$ and $d$ rounded to 1 decimal place: $c = 47.3$ and $d = 4.6$. We want to find the lower and upper bounds of the difference $c - d$.\n\n2. **Recall the bounds for rounding to 1 decimal place:**\nIf a number is rounded to 1 decimal place, the actual number lies within $\pm 0.05$ of the rounded value.\n\nSo, for $c = 47.3$, the bounds are:\n$$47.25 \leq c < 47.35$$\nFor $d = 4.6$, the bounds are:\n$$4.55 \leq d < 4.65$$\n\n3. **Calculate the lower bound of $c - d$:**\nThe smallest value of $c - d$ occurs when $c$ is at its minimum and $d$ is at its maximum:\n$$\text{Lower bound} = 47.25 - 4.65 = 42.6$$\n\n4. **Calculate the upper bound of $c - d$:**\nThe largest value of $c - d$ occurs when $c$ is at its maximum and $d$ is at its minimum:\n$$\text{Upper bound} = 47.35 - 4.55 = 42.8$$\n\n5. **Final answer:**\nThe lower and upper bounds of $c - d$ are:\n$$42.6 \leq c - d < 42.8$$