# How do you use scientific notation to express a lightyear in miles?

##### 1 Answer
Mar 25, 2015

I'll do it in meters - you can convert this yourself.

Speed of light $c = 299792458 m / s$ or in scientific notation:
$c = 2.99792458 \cdot {10}^{8} m / s$
We may round that to $2.998 \cdot {10}^{8}$

Multiply by
$3600 = 3.6 \cdot {10}^{3}$ (seconds in an hour)
$24 = 2.4 \cdot {10}^{1}$(hours in a day)
$365.25 = 3.6525 \cdot {10}^{2}$ (days in a year)

On your calculator you do this like:
$2.998 \cdot 3.6 \cdot 2.4 \cdot 3.6525 = 94.61 = 9.461 \cdot {10}^{1}$

Now add all the other exponents to this final ($1$) exponent
$8 + 3 + 1 + 2 + 1 = 15$

So the final answer $L y = 9.461 \cdot {10}^{15}$ meter
(just to make sure I checked with Wikipedia, and it checks)

It should be easy to do the same with miles
(your answer should be $\approx 5.9 \cdot {10}^{12}$ miles.