# Video: Converting between Light-Years and Meters

The Milky Way is about 100000 light-years in diameter. 1 light-year is equal to 9.46 × 10¹⁵ m. What is the diameter of the Milky Way in metres?

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### Video Transcript

The Milky Way is about 100000 light-years in diameter. One light-year is equal to 9.46 times 10 to the power of 15 metres. What is the diameter of the Milky Way in metres?

Okay, so this question is talking about the Milky Way which is the galaxy that we are in. Now, this galaxy is a spiral galaxy. But if we approximate it to be a circle, then we can say that the diameter, which is the distance from one end to the other end whilst going through the centre, is about 100000 light-years. So we can call the diameter 𝑑 and say that 𝑑 is equal to 100000 light-years. Now, we’ve also been told that one light-year is equal to 9.46 times 10 to the power of 15 metres. And we’ve been asked to find the diameter of the Milky Way in metres.

So one light-year is 9.46 times 10 to the power of 15 metres. And the diameter of the Milky Way is 100000 lots of this distance. So we can say that the diameter 𝑑 is equal to 100000 multiplied by one light-year which is the same thing as 9.46 times 10 to the power of 15 metres. Therefore, we’ve taken the unit of light-year and, instead, we’ve substituted in this value. Then when we evaluate the right-hand side of this equation, we can, first of all, see that we can write 100000 as 10 to the power of five. And then we can multiply 10 to the power of five by this number here.

All we’ll be doing then is adding the exponent five over here to this 15 over here. Because when we’ve got the same base, that’s 10, in both cases with different exponents and we multiply these two numbers together, then the exponents add together. And so, what we’re left with is 9.46 multiplied by 10 to the power of 15 plus five. And so, our final answer is that the diameter of the Milky Way in metres is 9.46 times 10 to the power of 20 metres.