Light travels approximately

5.87 X 10^12 miles in one year. This distance is called a light year. Suppose a star is 2 X 10^4 light years away. How many miles away is that star?

Please help with detailed steps to solve problem. Thanks.

2 x 10^4 light years x (5.87 x 10^12 miles/light year) = ??

Thanks Dr. Bob222.

To convert the distance in light years to miles, we can multiply the given distance in light years by the distance light travels in one year.

Step 1: Write down the given distance in light years: 2 X 10^4 light years.
Step 2: Write down the conversion factor: 5.87 X 10^12 miles per light year.
Step 3: Multiply the given distance by the conversion factor:

(2 X 10^4 light years) * (5.87 X 10^12 miles per light year)

Step 4: Multiply the numbers in front of the powers of 10: 2 * 5.87 = 11.74.
Step 5: Add the powers of 10: (10^4) * (10^12) = 10^(4+12) = 10^16.
Step 6: Multiply the results from steps 4 and 5: 11.74 * 10^16.

Step 7: Rewrite the result in scientific notation:
11.74 * 10^16 = 1.174 X 10^17.

Therefore, the star is approximately 1.174 X 10^17 miles away.

To find out how many miles away the star is, we need to multiply the distance traveled by light in one year (5.87 X 10^12 miles) by the number of light years the star is away (2 X 10^4 light years).

Step 1: Multiply the distance traveled by light in one year (5.87 X 10^12 miles) by the number of light years the star is away (2 X 10^4 light years).

5.87 X 10^12 miles * 2 X 10^4 light years

Step 2: Multiply the numbers outside the exponential notation:

5.87 * 2 = 11.74

Step 3: Add the exponents:

10^12 * 10^4 = 10^(12+4) = 10^16

Step 4: Multiply the result from step 2 with the result from step 3:

11.74 * 10^16 miles

Step 5: Convert the answer to scientific notation by moving the decimal point to the appropriate place. In this case, since 11.74 is greater than 1, we move the decimal point to the right, one place for each power of 10 in the exponent. In this case, we move it to the right 16 places.

1.174 * 10^17 miles

So, the star is approximately 1.174 * 10^17 miles away.