How to convert light years to km step by step

Asked by admin @ 22/11/2021 in Mathematics viewed by 260 People

A certain star is 4.3×10^2 light years from Earth. Pne light year is about 5.9×10^12 miles. How far from Earth (in miles) is the star? Express your answer in scientific notation.

Answered by admin @ 22/11/2021

Answer:

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.

$4.3\times10^2\hspace{2}lightyears\times\dfrac{5.9\times10^{12}miles}{1\hspace{2}lightyear}$

We cancel out the light years and then we are left with:

$(4.3\times10^2)\times(5.9\times10^{12}miles)$

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.

The answer will then be:

2.537 x 10¹⁵ miles

How to convert light years to km step by step

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