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Question

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

Solution

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We are given that 1 light year $\approx 5.9\times10^{12}\text{ miles}$ so:

$4.3\times 10^2\text{ light year}\cdot \dfrac{5.9\times 10^{12}\text{ miles}}{1\text{ light year}}$

Multiply $4.3$ and $5.9$ and round to 2 significant digits then add the exponents:

$\approx 25\times 10^{14}\text{ miles}$

This is not in scientific notation since the number is not between 0 and 10 so we move the decimal point by 1 place to the left. We then add 1 to the exponent to obtain the final answer:

$\approx\color{#c34632}2.5\times 10^{15}\text{ miles}$

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