The Sun, on average, is 93 million miles from Earth. How many ...

Question

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express

(b) using a metric prefix (km).

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem. The average distance between the earth and the moon is approximately 238,855 miles. Calculate this distance in meters and express it using a metric prefix kilometers. OK? So our end goal is to find the average distance or actually uh I should rephrase. So our end goal is to calculate the average distance between the earth and the moon into kilometers. OK. So it's given to us in miles. So we need to convert miles to meters and then meters to kilometers. So that is what we're gonna be doing. We're given some multiple choice answers. Also, they're also all on the same units of kilometers. So let's read them off to see what our final answer might be. A is 3.821 multiplied by 10 to the power of seven B is 3.821 multiplied by 10 to the power of five C is 83.844 multiplied by 10 to the power of seven and D is 3.844 multiplied by 10 to the power of five. OK. So first off, let us recall and use the dimensional analysis technique to help us convert miles to kilometers. So before we begin, let us recall and use the following conversion factors. So in one mile there is 1609.34 m. And in one kilometer, there is 1000 m. OK? So now we can perform dimensional analysis or our goal is to put, OK. So ultimately, our end goal is we want all the units to cancel out but kilometers because we're solving for our final answer, that's in kilometers. So let's do that. So we'll take our miles value which is 238 1008 155 miles. And we need to multiply it. I need to multiply it by. So this is using dimensional analysis. So in one mile, there is 1609.34 m. So the miles cancel out. So that's good. And now we need to note that in one kilometer there is 1000 meters. So we take our average distance between the earth and the moon and we multiply it by 1609.34 m divided by one mile, multiplied by one kilometer divided by 1000 m. So as you can see, miles, cancel out meters, cancel out, leaving us with kilometers, which is exactly what we're solving for. So when you plug that all into a calculator, we'll get 384,000, 398.9057 kilometers. But now we must round our answer for approximate precision. So we will say that our rounded value is 384 1004 100 kilometers. And now we need to write this rounded number into scientific notation. So let's do that. So to skip confusion, let's write it without a comma. So we'll have 384,400 which is the same as writing 384,400 0.0. So now we need to move our decimal place over. So we get one nonzero number to the left of the decimal. So let's move our decimal point. In this case, we have to move it to the left to get one nonzero value to the left of the decimal. So let's move our decimal place 12345. So it's gonna be 3.84 or because all the trailing zeros. So all the zeros coming after this are not considered significant. So we don't have to write it. So all we have to worry about is the 3.844. And we need to, as we know on power of 10 to some exponent value. In this case, definer exponent value, we need to consider how many places we move the decimal point to the left. So we moved our decimal place, five points to the left. So that means that the exponent value has to be five and it's positive because we move the decimal place to the left. Now, if we were moving it to the right, then it would be negative. But in this case, it is positive and don't forget our units which is kilometers and this is our final answer. So 3.844 multiplied by 10 to the power of five kilometers is our final answer. Hooray, we did it. So looking at our multiple choice answers, the correct answer has to be the letter D 3.8 or four multiplied by 10 to the power of five kilometers. And that is our final answer in scientific notation. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Struggling with Physics?

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express
(b) using a metric prefix (km).

Watch next

Introduction to Units practice set

Struggling with Physics?

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express(b) using a metric prefix (km).

Watch next

Introduction to Units practice set

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express
(b) using a metric prefix (km).