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Astronomers measure large distances in light-years. One light-year is the distance that lightcan travel in one year, or approximately 5.88 x 1012 miles. Suppose a star is 6.3 x 102 light years from Earth. In scientific notation, approximately how many miles is it ?
(6.3 * 10^2) * (5.88 * 10^12) = 37.044 * 10^14
= 3.7044 * 10^15
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To find the approximate number of miles, we can multiply the given distance in light-years by the distance that light can travel in one year (5.88 x 10^12 miles).
Let's solve it step-by-step:
1. Start with the given distance of the star from Earth, which is 6.3 x 10^2 light-years.
2. Multiply this distance by the distance that light can travel in one year (5.88 x 10^12 miles).
(6.3 x 10^2) * (5.88 x 10^12)
To multiply two numbers in scientific notation, we multiply the coefficients and add the exponents:
(6.3 * 5.88) x (10^2 * 10^12)
37.044 x 10^(2+12)
37.044 x 10^14
Now, the number is not in scientific notation anymore. We can convert it into scientific notation by moving the decimal point after the first non-zero digit, which is 3.7044.
Therefore, the approximate distance to the star in miles is 3.7044 x 10^15 miles.