Mars orbits the Sun at a distance of about 228 million kilometers. Assuming that Mars has a circular orbit, what is the distance traveled by the planet as it makes one full orbit around the Sun? Give your answer in scientific notation to one decimal place.
Okay, so this question is about Mars orbiting the Sun, and we are told to assume that Mars has a circular orbit. Let’s begin by drawing a diagram of the situation. In this sketch, this orange circle in the middle is the Sun, and this here is Mars. This pink circle shows the circular orbit of the planet. We are told that Mars orbits the Sun at a distance of about 228 million kilometers. This distance is the radius of the orbit, which we have marked on our diagram and labeled as 𝑟.
The question is asking us to work out the distance traveled by the planet as it makes one full orbit. Completing one full orbit means going one time around this circle. This means that the distance traveled by the planet in one full orbit is equal to the circumference of the circle. We can recall that the circumference 𝐶 of a circle is equal to two 𝜋 multiplied by the circle’s radius 𝑟. Since we know the radius for Mars’s orbit, then we can use this equation to work out the circumference. Subbing in the value of 𝑟 and evaluating this expression, we can calculate the value of the circumference 𝐶. This is clearly a big number, and it’s long to write it out like this.
When we have numbers like this one, it’s usually the convention to write them in scientific notation. In fact, if we look at the question, we see that we are asked to give our answer in scientific notation to one decimal place. In order to write this number in scientific notation, we need to move the decimal point one, two, three, four, five, six, seven, eight, nine places to the left. This means that the result becomes 1.432566 et cetera times 10 to the nine kilometers. The final step is to round this value to one decimal place. When we do this, we get our answer to the question that the distance traveled by the planet as it makes one full orbit around the Sun is equal to 1.4 times 10 to the nine kilometers.