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?
Understand the Problem
The question is asking to calculate the average distance from Venus to Mars when considering their distances from Earth, which are given in scientific notation. We will apply the concept of distances in space to find the total distance between Venus and Mars.
Answer
The average distance from Venus to Mars is \(2.00 \times 10^8\) kilometers.
Answer for screen readers
The average distance from Venus to Mars is (2.00 \times 10^8) kilometers.
Steps to Solve
- 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.
- 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) ]
- 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) ]
- 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} ]
- Final Check
Make sure that the units and powers of ten are consistent. The result is (2.00 \times 10^8) kilometers.
The average distance from Venus to Mars is (2.00 \times 10^8) kilometers.
More Information
This calculation is important for understanding distances in our solar system and highlights how scientific notation is useful for handling large values.
Tips
- Ignoring to convert the distances to the same power of ten before subtracting.
- Failing to align significant figures after subtraction.
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