1. ## Scientific Notation

One light-year is the distance light travels in a 365-day year. The speed of light is about 186,282.4 miles per second.

(a) How long is 1 light year in miles? Express your answer is scientific notation.

(b) Light from the North star takes 680 years to reach the earth. How many miles is the North star from earth?

2. a) $5.88 * 10^{12}$
b) $5,878,499,562,554*680 = 3.9973797 * 10^{15}$

above is the info. from google.

if you were to calculate it from the info given.

a) $186,282.4*60*60*24*7*52=5.86*10^{12}$
$part(a)*680 = 3.98*10^{15}$

3. ## but...

Originally Posted by BabyMilo
a) $5.88 * 10^{12}$
b) $5,878,499,562,554*680 = 3.9973797 * 10^{15}$

above is the info. from google.

if you were to calculate it from the info given.

a) $186,282.4*60*60*24*7*52=5.86*10^{12}$
$part(a)*680 = 3.98*10^{15}$
I could have searched google. I want to know how this is done manually?

Can you explain the algebra part more in detail?

4. Originally Posted by sologuitar
(a) How long is 1 light year in miles? Express your answer is scientific notation.
I don't think I can LaTeX this one up, so I'm going for a code block.

This is the unit analysis. I've used the computer format such as "3e8" to represent numbers in scientific notation such as $3 \times 10^8$.

Code:
         3e8 m   3600 s   24 hr   365 d    mile
1 year * ----- * ------ * ----- * ----- * ------
s       hr       d     year    1609 m
Years cancel out. So do s, hr, days, and meters. The only unit left is miles.

5. ## ok

Originally Posted by Haversine
I don't think I can LaTeX this one up, so I'm going for a code block.

This is the unit analysis. I've used the computer format such as "3e8" to represent numbers in scientific notation such as $3 \times 10^8$.

Code:
         3e8 m   3600 s   24 hr   365 d    mile
1 year * ----- * ------ * ----- * ----- * ------
s       hr       d     year    1609 m
Years cancel out. So do s, hr, days, and meters. The only unit left is miles.
Thank you.