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To find the lower and upper bounds of \( s \), we begin by determining the upper and lower bounds of \( d \) (distance) and \( t \) (time).

### Step 1: Identify significant figures
Given:
- \( d = 190 \) metres (2 significant figures)
- \( t = 8.1 \) seconds (2 significant figures)

### Step 2: Find the bounds
#### For \( d \):
- \( d = 190 \) metres to 2 significant figures means:
  - The lower bound \( d_{\text{lower}} = 185 \) metres
  - The upper bound \( d_{\text{upper}} = 195 \) metres

#### For \( t \):
- \( t = 8.1 \) seconds to 2 significant figures means:
  - The lower bound \( t_{\text{lower}} = 8.05 \) seconds
  - The upper bound \( t_{\text{upper}} = 8.15 \) seconds

### Step 3: Calculate speed \( s = \frac{d}{t} \)
#### Upper bound of \( s \):
The upper bound of \( s \) occurs when \( d \) is at its maximum and \( t \) is at its minimum:
\[
s_{\text{upper}} = \frac{d_{\text{upper}}}{t_{\text{lower}}} = \frac{195}{8.05}
\]

#### Lower bound of \( s \):
The lower bound of \( s \) occurs when \( d \) is at its minimum and \( t \) is at its maximum:
\[
s_{\text{lower}} = \frac{d_{\text{lower}}}{t_{\text{upper}}} = \frac{185}{8.15}
\]

Let's calculate these values to 3 significant figures.The lower bound of \( s \) is approximately \( 22.7 \, \text{m/s} \), and the upper bound of \( s \) is approximately \( 24.2 \, \text{m/s} \), both rounded to 3 significant figures.

Would you like further details or explanations?

Here are 5 related questions for further practice:
1. How do significant figures impact the accuracy of your final answer?
2. What would happen to the upper and lower bounds of \( s \) if \( d \) was measured to 3 significant figures instead?
3. Can you calculate the percentage error introduced by rounding \( d \) and \( t \) to their respective significant figures?
4. How would you find the bounds if \( s \) was calculated using a different formula, such as acceleration?
5. What are the implications of having large ranges in upper and lower bounds in real-world applications?

**Tip:** Always pay close attention to significant figures as they directly affect the precision of your calculated results.

A formula connecting speed (s), distance (d), and time (t) is s = d/t. Calculate the lower and upper bounds of s given that d = 190 metres to 2 significant figures and t = 8.1 seconds to 2 significant figures. Give your answers to 3 significant figures.

Learn how to calculate the upper and lower bounds of speed given distance and time with significant figures. This problem uses the formula s = d/t, where d is 190 meters and t is 8.1 seconds, both rounded to 2 significant figures. Suitable for students in Grades 10-12.

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