What is the representative fraction of 10km to 20cm?
Understand the Problem
The question is asking for the representative fraction (RF) which is a ratio that expresses the relationship between a distance on a map and the corresponding distance on the ground. Here, we need to convert 10 kilometers into centimeters and then form the ratio with 20 centimeters.
Answer
The representative fraction (RF) is $\frac{1}{50,000}$.
Answer for screen readers
The representative fraction (RF) is $\frac{1}{50,000}$.
Steps to Solve
- Convert kilometers to centimeters
Since we need to convert 10 kilometers into centimeters, we will use the conversion factor that 1 kilometer is equal to 100,000 centimeters.
The calculation is:
$$ 10 \text{ km} \times 100,000 \frac{\text{cm}}{\text{km}} = 1,000,000 \text{ cm} $$
- Form the ratio
Now that we have the distance in centimeters on the ground (1,000,000 cm), we can form the ratio with the distance on the map (20 cm).
The ratio is expressed as:
$$ \text{RF} = \frac{\text{Distance on map}}{\text{Distance on ground}} $$
Substituting our values gives us:
$$ \text{RF} = \frac{20 \text{ cm}}{1,000,000 \text{ cm}} $$
- Simplify the ratio
To simplify the fraction, we divide both the numerator and the denominator by 20:
$$ \text{RF} = \frac{20 \div 20}{1,000,000 \div 20} = \frac{1}{50,000} $$
The representative fraction (RF) is $\frac{1}{50,000}$.
More Information
The representative fraction provides a scale for the map, helping users understand that 1 unit on the map represents 50,000 units in reality. This ratio helps in measuring distances on maps accurately.
Tips
- Incorrect unit conversion: Make sure to convert kilometers to centimeters correctly. Remember that 1 km = 100,000 cm.
- Not simplifying the ratio: Always check if the ratio can be simplified for clarity.
AI-generated content may contain errors. Please verify critical information
