Express 5008 kilometres in scientific notation, using a coefficient between 1 and 10 multiplied by an appropriate power of 10.

Introduction / Context:
Scientific notation is a standard way of writing very large or very small numbers as a product of a number between 1 and 10 and an integer power of 10. It is widely used in science and engineering for clear and compact representation. Here we need to express 5008 kilometres in proper scientific notation, ensuring the coefficient is between 1 and 10 and the power of 10 is chosen correctly.

Given Data / Assumptions:
- The number to be converted is 5008 km.
- Scientific notation has the form c × 10^n where 1 ≤ c < 10 and n is an integer.
- We must keep the units in kilometres, not convert to metres or other units.

Concept / Approach:
To write 5008 in scientific notation, we move the decimal point so that there is exactly one non-zero digit to the left of the decimal point. We count how many places the decimal point moves to determine the exponent of 10. Moving the decimal to the left increases the exponent; moving it to the right would decrease it. We then attach the unit km back to the final expression.

Step-by-Step Solution:
Step 1: Write 5008 as a decimal number: 5008.0. Step 2: Move the decimal point to obtain a number between 1 and 10. Placing the decimal after the first digit 5 gives 5.008. Step 3: Count how many places the decimal moved: from 5008.0 to 5.008, the decimal moves 3 places to the left. Step 4: Moving 3 places to the left corresponds to multiplying by 10^3. So 5008 = 5.008 × 10^3. Step 5: Attach the unit: 5008 km = 5.008 × 10^3 km.

Verification / Alternative check:
We can verify by reversing the process: 5.008 × 10^3 = 5.008 × 1000 = 5008, because 5.008 × 1000 shifts the decimal three places to the right. The value is restored exactly to 5008, so the scientific notation is correct. The coefficient 5.008 satisfies 1 ≤ 5.008 < 10, so the form is valid.

Why Other Options Are Wrong:
Option 50.08 × 10^3 km: Here the coefficient 50.08 is not between 1 and 10, so this is not proper scientific notation.
Option 5.008 × 10^-3 km: This represents 0.005008 km, which is much smaller than 5008 km and therefore incorrect as a representation of 5008 km.
Option 500.8 × 10^3 km: This equals 500800 km, which is different from 5008 km by a factor of 100, so it is wrong.
Option None of these: Incorrect because 5.008 × 10^3 km is a valid option and correctly represents 5008 km in scientific notation.

Common Pitfalls:
One frequent mistake is to stop after writing 50.08 × 10^2, which is numerically correct but not in proper scientific notation because the coefficient is greater than 10. Another error is to miscount the number of decimal places moved, resulting in the wrong power of 10. Always ensure that the coefficient is between 1 and 10 and then verify by reversing the conversion.

Final Answer:
5008 km written in scientific notation is 5.008 × 10^3 km.