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We are given two numbers, \( f \) and \( g \), rounded to one decimal place, and we are tasked with finding the lower and upper bounds for the difference \( f - g \).

### Step-by-step approach:

1. **Number \( f \) rounded to 1 decimal place is 49.2**.
   - The lower bound of \( f \) is \( 49.15 \) (since it could be as low as 49.15, rounded up to 49.2).
   - The upper bound of \( f \) is \( 49.25 \) (since it could be as high as 49.25, rounded down to 49.2).

2. **Number \( g \) rounded to 1 decimal place is 7.8**.
   - The lower bound of \( g \) is \( 7.75 \) (since it could be as low as 7.75, rounded up to 7.8).
   - The upper bound of \( g \) is \( 7.85 \) (since it could be as high as 7.85, rounded down to 7.8).

### Finding the bounds for \( f - g \):

- **Lower bound of \( f - g \):**
   \[
   \text{Lower bound} = \text{Lower bound of } f - \text{Upper bound of } g = 49.15 - 7.85 = 41.30
   \]

- **Upper bound of \( f - g \):**
   \[
   \text{Upper bound} = \text{Upper bound of } f - \text{Lower bound of } g = 49.25 - 7.75 = 41.50
   \]

### Final Answer:
- The lower bound of \( f - g \) is 41.30.
- The upper bound of \( f - g \) is 41.50.

Would you like further clarification or more details on any part of the process?

Here are 5 related questions to further expand your understanding:
1. How are upper and lower bounds affected by the number of decimal places?
2. What would happen to the bounds if both numbers were rounded to 2 decimal places instead of 1?
3. How do you calculate the bounds if you are given the product \( f \times g \)?
4. What is the significance of choosing the largest and smallest possible values when calculating bounds?
5. Can you apply this concept of bounds to measurements in physics, such as error margins?

**Tip:** When calculating upper and lower bounds, always subtract the largest possible value of the second number from the smallest possible value of the first, and vice versa, to ensure correct bounds.

A number, f, rounded to 1 d.p. is 49.2. Another number, g, rounded to 1 d.p. is 7.8. What are the lower and upper bounds of f - g?

Learn how to find the lower and upper bounds of f - g when f is rounded to 49.2 and g is rounded to 7.8, both to 1 decimal place. This step-by-step solution is suitable for students in Grades 7-9 and covers key concepts such as rounding, bounds, and subtraction.

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