To solve this problem, we need to understand how the faulty odometer works. The faulty odometer skips the digits 4 and 6, meaning it doesn't count numbers containing these digits.

This implies that the sequence of numbers counted by the odometer uses a base-8 system (octal) with digits 0, 1, 2, 3, 5, 7, 8, and 9. Our goal is to convert the faulty reading of 2500 in this modified system into its actual decimal value.

Conversion Steps:

1. Understand the Faulty Base:

   • In a normal decimal system, each digit represents a power of 10. However, in this faulty odometer system, each digit represents a power of 8 (because it skips two digits).

2. Convert from Faulty Base-8 to Decimal:

   • The faulty odometer reading is 2500.
   • To convert from this faulty base-8 to decimal, interpret 2500 as an octal number: $2500_{\text{(faulty)}} = 2 \cdot 8^3 + 5 \cdot 8^2 + 0 \cdot 8^1 + 0 \cdot 8^0$

3. Calculate Each Term:

   • $2 \cdot 8^3 = 2 \cdot 512 = 1024$
   • $5 \cdot 8^2 = 5 \cdot 64 = 320$
   • $0 \cdot 8^1 = 0$
   • $0 \cdot 8^0 = 0$

4. Sum the Values: $1024 + 320 + 0 + 0 = 1344$

Thus, the car has actually traveled 1344 kilometers.

If you have further questions or need detailed explanations, feel free to ask!

Related Questions:

1. How does the base-8 system differ from the base-10 system?
2. Can we calculate the distance for a different odometer reading with the same fault?
3. What would be the faulty reading if the car traveled 1344 km and then the odometer was fixed?
4. How does skipping certain digits affect number representation?
5. How do odometer faults typically impact vehicle maintenance records?
6. How can similar problems be solved if more digits are skipped in the odometer?
7. What is the mathematical method to convert octal numbers to decimal?
8. How does the inclusion or exclusion of digits change the base of a number system?

Tip: When working with non-standard number systems, identify the base and ensure all digits conform to it.