Question

A certain star is 4.6 x 10^2 light years from the Earth. One light year is about 5.9 x 10^12 miles. How far from the earth​ (in miles) is the​ star? Has to be answered in scientific notation

1. thnahdat

What the person said above

2. bonexptip
2.537 x 10¹⁵ miles
Step-by-step explanation:
We are given the following:
1 light year = 5.9 x 10¹² miles
Distance of the star = 4.3 x 10² light years
To get this we just convert the distance of the star in light years into miles.
We cancel out the light years and then we are left with:
In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.
Coefficients:
4.3 x 5.9 = 25.37
Exponents of 10:
10² x 10¹² = 10⁽²⁺¹²⁾=10¹⁴
Then we combine them again to form a scientific notation:
25.37 x 10¹⁴
But since the standard in writing a scientific notation, the coefficient needs to be a number from 1-9, we need to move the decimal. When we move the decimal to the right or left, we change the exponent of the power of 10. Since we will move it once to the left, we add 1.