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

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

Explanation:

As given

Distances in space are measured in light-years.

`The\ distance\ from\ Earth\ to\ a\ star\ is\ 4.1* 10^(13)\kilometers.`

`1 light-year = 9.46* 10^(12)\ kilometers`

As

`1\ kilometer = (1)/(9.46* 10^(12)) \ light\ years`

Thus

`4.1* 10^(13)\ kilometer = (4.1* 10^(13))/(9.46* 10^(12)) \ light\ years`

by using the exponent property .

`(x^(a))/(x^(b)) = x^(a-b)`

`4.1* 10^(13)\ kilometer =0.433* 10^(13-12) \ light\ years`

`4.1* 10^(13)\ kilometer =0.433* 10^(1) \ light\ years`

`4.1* 10^(13)\ kilometer =(433)/(1000) * 10^(1) \ light\ years`

`4.1* 10^(13)\ kilometer =(433)/(100)\ light\ years`

`4.1* 10^(13)\ kilometer = 4.33\ light\ years`

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