Question

Proxima Centauri, the star nearest to our solar system, is 4.3 light-years away. Use the information in Exercise 87(a) to express this distance in miles.

Short answer

The required distance is$2.537\times {10}^{13}mi$.

Step-by-step solution

Step 1. Scientific Notation.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$and n is an integer.

Step 2. Determine the expression.

It is given that a light-year, the distance that light travels in one year, is about 5,900,000,000,000 mi.

Also, the Proxima Centauri, the star nearest to our solar system, is 4.3 light-years away.

The required expression is:$5,900,000,000,000\times 4.3mi$

Step 3. Determine the distance.

Rewrite the given expression

Move the decimal point 12 places left to create a new number from 1 up to 10.

We move decimal 12 times; also, because we moved the decimal to the left, the exponent is positive.

$\begin{array}{l}5,900,000,000,000\times 4.3mi=5.9\times 4.3\times {10}^{12}mi\\ =25.37\times {10}^{12}mi\\ =2.537\times {10}^{13}mi\end{array}$