5. One light-year is nearly $6 \times 10^{12}$ miles. In 2016 , the Hubble Space Telescope set a new cosmic record, observing a galaxy 13.4 thousand million light-years away.
Roughly how many miles is that?
A $8 \times 10^{20}$
B $8 \times 10^{21}$
C $8 \times 10^{22}$
D $8 \times 10^{23}$
E $8 \times 10^{24}$
SolUTION
C
One thousand million is $1000 \times 1000000=10^{3} \times 10^{6}=10^{3+6}=10^{9}$. Therefore 13.4 thousand million light-years is $13.4 \times 10^{9}$ light-years. Therefore, because a light-year is nearly $6 \times 10^{12}$ miles, 13.4 thousand million light-years is approximately
$$
\left(6 \times 10^{12}\right) \times\left(13.4 \times 10^{9}\right) \text { light-years. }
$$

Now
$$
\left(6 \times 10^{12}\right) \times\left(13.4 \times 10^{9}\right)=(6 \times 13.4) \times\left(10^{12} \times 10^{9}\right) .
$$

Now $6 \times 13.4$ is approximately 80 , therefore, $(6 \times 13.4) \times\left(10^{12} \times 10^{9}\right)$ is approximately
$$
80 \times\left(10^{12} \times 10^{9}\right) \text {. }
$$

Finally, we have
$$
80 \times\left(10^{12} \times 10^{9}\right)=8 \times 10 \times 10^{12+9}=8 \times 10 \times 10^{21}=8 \times 10^{22} .
$$

Therefore 13.4 thousand million light-years is approximately $8 \times 10^{22}$ miles.