The planet Venus is on average 2.5 x 10^7 kilometers from Earth. The planet Mars is on average 2.25 x 10^8 kilometers from Earth. When Venus, Earth, and Mars are aligned, what is t... The planet Venus is on average 2.5 x 10^7 kilometers from Earth. The planet Mars is on average 2.25 x 10^8 kilometers from Earth. When Venus, Earth, and Mars are aligned, what is the average distance from Venus to Mars? Read more

Steps to Solve

1. Identify Distances in Scientific Notation

The average distance from Earth to Venus is given as (2.5 \times 10^7) kilometers, and the distance from Earth to Mars is (2.25 \times 10^8) kilometers.

2. Calculate the Average Distance Between Venus and Mars

To find the average distance from Venus to Mars, we first calculate the distance from Venus to Mars as: [ \text{Distance}{\text{Venus to Mars}} = \text{Distance}{\text{Earth to Mars}} - \text{Distance}_{\text{Earth to Venus}} ]

This can be represented as: [ \text{Distance}_{\text{Venus to Mars}} = (2.25 \times 10^8) - (2.5 \times 10^7) ]

3. Make the Exponents the Same

Convert (2.5 \times 10^7) to the same exponent as (2.25 \times 10^8): [ 2.5 \times 10^7 = 0.25 \times 10^8 ]

Now the equation becomes: [ \text{Distance}_{\text{Venus to Mars}} = (2.25 \times 10^8) - (0.25 \times 10^8) ]

4. Perform the Subtraction

Now we can subtract the two distances: [ \text{Distance}_{\text{Venus to Mars}} = (2.25 - 0.25) \times 10^8 = 2.00 \times 10^8 \text{ kilometers} ]

5. Final Check

Make sure that the units and powers of ten are consistent. The result is (2.00 \times 10^8) kilometers.