# Miles In Light Year

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#### mathdad

##### Full Member
One light-year is defined by astronomers to be the distance that a beam of light will travel in one year aka 365 days. If the speed of light is 186,000 miles per second, how many miles are in a light year? Two light years? Express your answer in scientific notation.

What is the set for this problem? I am lost.

#### Dr.Peterson

##### Elite Member
What is the setup? Distance = rate * time.

How many miles will an object go in 365 days at a speed of 186,000 miles per second? Find the number of hours in 365 days, and the number of seconds in an hour, and multiply. You may want to look up information about unit conversions, particularly the "unit factor" method (which goes by many names).

Now please show where you are lost. Or at least describe what you see from your location, if you don't know where you are.

#### mathdad

##### Full Member
What is the setup? Distance = rate * time.

How many miles will an object go in 365 days at a speed of 186,000 miles per second? Find the number of hours in 365 days, and the number of seconds in an hour, and multiply. You may want to look up information about unit conversions, particularly the "unit factor" method (which goes by many names).

Now please show where you are lost. Or at least describe what you see from your location, if you don't know where you are.

How many miles will an object go in 365 days at a speed of 186,000 miles per second? Find the number of hours in 365 days, and the number of seconds in an hour, and multiply.

Solution:

One day = 24 hours
365 days = 365(24) = 8,760 hours

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1 minute = 60 seconds
1 hour = 60(60) = 3600 seconds
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Seconds in one year =
8760(3600) = 31,536,000

Do I now multiply
31,536,000 by 186,000 and then convert to scientific notation?

#### Dr.Peterson

##### Elite Member
Yes. You've done this:

$$\displaystyle \frac{365\text{ days}}{1}\cdot\frac{24\text{ hours}}{1\text{ day}}\cdot\frac{3600\text{ sec}}{1\text{ hour}}\cdot\frac{186,000\text{ miles}}{1\text{ sec}}$$

#### mathdad

##### Full Member
Yes. You've done this:

$$\displaystyle \frac{365\text{ days}}{1}\cdot\frac{24\text{ hours}}{1\text{ day}}\cdot\frac{3600\text{ sec}}{1\text{ hour}}\cdot\frac{186,000\text{ miles}}{1\text{ sec}}$$
Great. Can you answer the question in full? I want use it as reference to solve others just like it.

#### topsquark

##### Full Member
He just gave you 90% of the problem. Surely you can finish the rest?

-Dan

#### mathdad

##### Full Member
He just gave you 90% of the problem. Surely you can finish the rest?

-Dan
Yes. I will finish on paper.

#### mathdad

##### Full Member
Here is a slightly different approach on paper. I decided to use v for velocity for the formula d = vt.

Note: I simply switched from d = rt to
d = vt.

t = 365 days x 24hrs/day x 60 min/h x 60 s/min = 31,536,000 seconds
v = 186,000 miles per seconds

d = vt = (31,536,000 s)(186,000 mps) = 5.865696 x 10^12 miles

I say there are 5.865696 x 10^12 miles in one light year.

Two light years:

2 light years x 5.865696 x 10^12/ light years = 1.1731392 x 10^13 miles.

Correct?

#### Dr.Peterson

##### Elite Member
Correct.

If the context were one in which significant digits were taken into account, you would want to round to 5.87 * 10^12 miles and 1.17 * 10^13 miles, because 365 and 186,000 are round numbers (3 significant digits each).

#### mathdad

##### Full Member
Correct.

If the context were one in which significant digits were taken into account, you would want to round to 5.87 * 10^12 miles and 1.17 * 10^13 miles, because 365 and 186,000 are round numbers (3 significant digits each).
Very cool. Another one for the files.

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