Answer: The star is 2 quadrillion( 1 followed by 15 zeroes) and 301 trillion( 1 followed by 12 zeroes) miles away from Earth. To shorten this into scientific notation(the format used to write large numbers) is: 2.301 x 10^15.
Step-by-step explanation: First, find the exact value of the units of measurement, which in this case is light years. To do so, your best choice would be to separate the equation given for light years. (Note: the line through the middle is just to separate two very similar series of steps.)
1. 5.9 x 10^12 into 5.9 x (10^12)
2. 10^12 = 1,000,000,000,000. 10^12 is the same as adding 11 zeroes since it is multiplying by tens, not 12 zeroes since there is already a zero on the ten. This number is one-trillion(we will shorten this number to 1T).
3. 5.9 x 1T = 5.9 T. Don't get nervous of the big numbers, this is the same as doing 5.9 x 1 and then adding a name afterwards. Now that we have our number, we must remember the question is asking for miles, so keep in mind this large number is the miles.
4. 5.9T --> 5.9 | T Take off the T from 5.9T for now to make this problem a little simpler for this next part.(Note: the | is a separator)
------------------------------------------------------------------------------------------------------------- 5. 3.9 x 10^2 into 3.9 x (10^2)
6. 10^2 = 100. 10^2 is the same as multiplying adding one zero to the ten. This number is one-hundred.
7. 3.9 x 100 = 390. Please remember that this step is to find the number of light years away from the Earth.
8. 390 x 5.9 = 2301. This is the number of lightyears times the number of miles without the zeroes. The next step is to add the zeroes which brings the number into trillions.
9. 2301 | T --> 2301T. Next is to simplify this number, since every zero after 3 makes the number into a different name, this number is now has 15 zeroes. This number(one-quadrillion) will be shortened to Qu.
10-ish. 2301T = 2.301Qu. This is the name of a number with 15-17 zeroes.
10. 2.301Qu = 2.301 x 10^15. This is just turning the number into scientific notation.
Done!