Let's work through the problem step-by-step to determine the petrol consumption [tex]\( c \)[/tex] for David's journey, taking into account the significant figures.
### Step 1: Determine the Range of [tex]\( d \)[/tex] and [tex]\( p \)[/tex]
David's distance [tex]\( d \)[/tex] is reported as 187 km (correct to 3 significant figures). This means that:
1. The lower bound for [tex]\( d \)[/tex] is [tex]\( 186.5 \)[/tex] km.
2. The upper bound for [tex]\( d \)[/tex] is [tex]\( 187.5 \)[/tex] km.
The petrol used [tex]\( p \)[/tex] is reported as 28 litres (correct to 2 significant figures). This means that:
1. The lower bound for [tex]\( p \)[/tex] is [tex]\( 27.5 \)[/tex] litres.
2. The upper bound for [tex]\( p \)[/tex] is [tex]\( 28.5 \)[/tex] litres.
### Step 2: Calculate the Boundaries for [tex]\( c \)[/tex]
The petrol consumption [tex]\( c \)[/tex] is given by [tex]\( \frac{d}{p} \)[/tex].
1. Lower bound of [tex]\( c \)[/tex]:
Use the lower bound of [tex]\( d \)[/tex] and upper bound of [tex]\( p \)[/tex]:
[tex]\[
c_{\text{lower}} = \frac{186.5}{28.5} \approx 6.543859649
\][/tex]
2. Upper bound of [tex]\( c \)[/tex]:
Use the upper bound of [tex]\( d \)[/tex] and lower bound of [tex]\( p \)[/tex]:
[tex]\[
c_{\text{upper}} = \frac{187.5}{27.5} \approx 6.818181818
\][/tex]
### Step 3: Calculate the Average Value for [tex]\( c \)[/tex]
Using the average values of [tex]\( d \)[/tex] and [tex]\( p \)[/tex]:
[tex]\[
c_{\text{average}} = \frac{d}{p} = \frac{187}{28} \approx 6.678571429
\][/tex]
### Step 4: Determine the Final Answer with Reasoning
Given the bounds:
- The lower bound of [tex]\( c \)[/tex] is approximately [tex]\( 6.543859649 \)[/tex] km/litre.
- The upper bound of [tex]\( c \)[/tex] is approximately [tex]\( 6.818181818 \)[/tex] km/litre.
Since the values of [tex]\( d \)[/tex] and [tex]\( p \)[/tex] are to 3 and 2 significant figures respectively, it is reasonable to report the consumption [tex]\( c \)[/tex] to an appropriate degree of precision, which should also be to 3 significant figures given the context.
Thus, the petrol consumption [tex]\( c \)[/tex] for David’s journey, rounded to three significant figures, is:
[tex]\[
c \approx 6.68 \, \text{km/litre}
\][/tex]
This solution is based on considering the significant figures and the calculated values for [tex]\( c \)[/tex] and justifies that [tex]\( 6.68 \, \text{km/litre} \)[/tex] is an appropriate representation of the average petrol consumption.
