Alright class, let’s tackle this problem step-by-step to find the most accurate approximations for converting gas prices from liters to gallons.
### Step 1: Understand the Conversion Factor
We know that 1 liter is equivalent to approximately 0.264 gallons. This means that to convert a price per liter to a price per gallon, we need to divide the price per liter by 0.264.
### Step 2: Convert the Price from Liters to Gallons
The given price of gas in Canada is $1.22 per liter. We wish to convert this price to the price per gallon using the conversion factor.
[tex]\[
\text{Price per gallon} = \frac{\text{Price per liter}}{\text{Conversion factor}}
\][/tex]
Substitute the given values:
[tex]\[
\text{Price per gallon} = \frac{1.22}{0.264} \approx 4.621
\][/tex]
Thus, the price per gallon is approximately $4.621.
### Step 3: Find Two Suitable Approximations
The problem hints that we should consider two approximations to find which ones are most accurate. The approximations we evaluate are those that come closest to the actual converted price of $4.621 per gallon.
We will check two potential approximations that involve slightly different divisors:
1. Approximating by dividing by 0.26
2. Approximating by dividing by 0.27
### Step 4: Calculate Each Approximation
#### Approximation 1: Divide by 0.26
[tex]\[
\text{Approximation 1} = \frac{1.22}{0.26} \approx 4.692
\][/tex]
#### Approximation 2: Divide by 0.27
[tex]\[
\text{Approximation 2} = \frac{1.22}{0.27} \approx 4.519
\][/tex]
### Step 5: Compare and Select the Most Accurate Approximations
We compare the obtained approximations to the actual price per gallon calculated earlier ($4.621):
- Approximation 1: $4.69
- Approximation 2: $4.52
Both approximations are close, but based on the values:
- Approximation 1 is closer to the actual price per gallon ([tex]$4.621) as it’s only a difference of about $[/tex]0.07.
- Approximation 2 also provides a suitable approximation but it is slightly further off with a difference of about $0.10.
### Conclusion
After evaluating the results:
1. The price per gallon is approximately $4.621.
2. The two most accurate approximations for converting prices from liters to gallons are [tex]$4.69 (using 0.26) and $[/tex]4.52 (using 0.27).
This concludes our step-by-step solution. Are there any questions about today's lesson?
