Let’s solve this problem step by step.

Step 1: Understand the rounding

• A number rounded to 1 decimal place (1 d.p.) could vary by ±0.05 from its rounded value.
  • For $a = 49.3$, its true value lies in the range: $49.25 \leq a < 49.35$
  • For $b = 7.6$, its true value lies in the range: $7.55 \leq b < 7.65$

Step 2: Compute the bounds for $a - b$

The difference $a - b$ will have the following:

• Minimum value: When $a$ is at its lower bound (49.25) and $b$ is at its upper bound (7.65): $\text{Minimum } (a - b) = 49.25 - 7.65 = 41.6$
• Maximum value: When $a$ is at its upper bound (49.35) and $b$ is at its lower bound (7.55): $\text{Maximum } (a - b) = 49.35 - 7.55 = 41.8$

Final Answer:

The lower and upper bounds of $a - b$ are: $41.6 \leq a - b < 41.8$

Would you like further clarification or details on how to handle similar problems?

Related Questions:

1. How are bounds affected when rounding to 2 decimal places instead of 1?
2. Can $a - b$ ever equal exactly 41.7 in this scenario?
3. How do we compute bounds for addition $a + b$?
4. What happens if both $a$ and $b$ are rounded to whole numbers instead?
5. How does rounding impact calculations in practical scenarios?

Tip:

When dealing with bounds, always calculate extremes (minimum and maximum) by combining the smallest and largest possible values strategically.