Question

Distances in space are measured in light-years. The distance from Earth to a star is 4.1 × 1013 kilometers. What is the distance, in light-years, from Earth to the star (1 light-year = 9.46 × 1012 kilometers)?
0.23 light-year
2.36 light-years
4.33 light-years
5.36 light-years

Answer 1

How many 'light years distance' can fit in the distance from earth to the star

So we have to divide:

4.1 x 10^13 / 9.46 x 10^12 = 4.33

Answer 2

Answer:

The distance, in light-years, from Earth to the star is 4.33 light- years.

Step-by-step explanation:

As given

Distances in space are measured in light-years.

$The\ distance\ from\ Earth\ to\ a\ star\ is\ 4.1\times 10^{13}\kilometers.$

$1 light-year = 9.46\times 10^{12}\ kilometers$

As

$1\ kilometer = \frac{1}{9.46\times 10^{12}} \ light\ years$

Thus

$4.1\times 10^{13}\ kilometer = \frac{4.1\times 10^{13}}{9.46\times 10^{12}} \ light\ years$

by using the exponent property .

$\frac{x^{a}}{x^{b}} = x^{a-b}$

$4.1\times 10^{13}\ kilometer =0.433\times 10^{13-12} \ light\ years$

$4.1\times 10^{13}\ kilometer =0.433\times 10^{1} \ light\ years$

$4.1\times 10^{13}\ kilometer =\frac{433}{1000} \times 10^{1} \ light\ years$

$4.1\times 10^{13}\ kilometer =\frac{433}{100}\ light\ years$

$4.1\times 10^{13}\ kilometer = 4.33\ light\ years$

Therefore the distance, in light-years, from Earth to the star is 4.33 light- years.