Answer
There are about $5.87\times 10^{12}$ miles in one light-year.
Work Step by Step
The number of seconds in a year is $60\cdot 60\cdot 24\cdot 365$.
The number of miles covered by light in a year is
$186,000\cdot(60\cdot 60\cdot 24\cdot 365)=$
... write each factor in scientific notation
$=(1.86\times 10^{5})(6\times 10^{1})^{2}(2.4\times 10^{1})(3.65\times 10^{2})$
... The product of the decimal numbers is $586.5696$,
... the sum of exponents of powers of ten is 10
$=586.5696\times 10^{10}$
...adjust the decimal point so there is one non-zero digit left of it.
...it moved two places, so multiply with $10^{-2}.$
... which is why we multiply $10^{10}$ with $10^{2}$
$=5.865696\times 10^{12}$
$\approx 5.87\times 10^{12}$
There are about $5.87\times 10^{12}$ miles in one light-year.
