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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 5.9×1012 miles\approx 5.9\times10^{12}\text{ miles} so:

4.3×102 light year5.9×1012 miles1 light year4.3\times 10^2\text{ light year}\cdot \dfrac{5.9\times 10^{12}\text{ miles}}{1\text{ light year}}

Multiply 4.34.3 and 5.95.9 and round to 2 significant digits then add the exponents:

25×1014 miles\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:

2.5×1015 miles\approx\color{#c34632}2.5\times 10^{15}\text{ miles}

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