Show work. Simplify.
A light-year is 9.46x10^12 in Km or 6 trillion miles per year (6x10^12)
Problem:
Saturn is 989.64 Million miles at its closest distance. Find the distance in light years.
989.64million= _____ x 10_ LY d= _____ x 10_ / 6 trillion
(blank? times 10 power? LY d= blank? times 10 power?
divided by 6 trillion)
Thank you!
To find the distance from miles to light years, you need to divide the number of miles by the conversion factor of 6 trillion miles per light year.
Let's perform the calculations step by step:
1. Start with the given distance of 989.64 million miles.
Therefore, d = 989.64 million.
2. Divide the distance by the conversion factor of 6 trillion miles per light year.
d = 989.64 million / 6 trillion.
3. Simplify both the numerator and denominator by converting them to scientific notation.
989.64 million becomes 9.8964 x 10^8.
6 trillion becomes 6 x 10^12.
4. Substitute the values into the formula:
d = (9.8964 x 10^8) / (6 x 10^12).
5. When dividing terms with the same base, subtract the exponent in the denominator from the exponent in the numerator.
d = (9.8964 / 6) x (10^8 / 10^12).
6. Simplify the base by performing the division:
d = 1.6494 x (10^8 / 10^12).
7. Subtract the exponents:
d = 1.6494 x 10^(8-12).
8. Subtract the exponents at the top:
d = 1.6494 x 10^(-4).
Therefore, the distance from Saturn to Earth in light years is approximately 1.6494 x 10^(-4) light years.