Number of Miles In One Light Year

[felizgu]

TL;DR Summary: This is an astronomy application.

One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year (365 days). If the speed of light is 186,000 miles per second, how many miles are in a light-year? Express your answer in scientific notation.

Let me see.

24 hours in one day.

3600 seconds in one hour.

24 x 3600 = 86,400 seconds in one day.

365 x 86,400 = 31,536,000

31,536,000 x 186,000 = 5,865,696,000,000

1. Is this right?

2. If it is right, how do I express my answer in scientific notation?

 

[hutchphd]

Please be aware that the 365 days in a year is an approximate number (good to ~3 sig fig so the appropriate scientific notation answer would be $$1~LIGHT~YEAR~=5.87x10^{12} mi$$. There is probably an official value certified by the ministry of unfathomable distances........

 

[felizgu]

Please be aware that the 365 days in a year is an approximate number (good to ~3 sig fig so the appropriate scientific notation answer would be $$1~LIGHT~YEAR~=5.87x10^{12} mi$$. There is probably an official value certified by the ministry of unfathomable distances........

Do I multiply 93 x 10^(6) by 5.87 x 10^(12) to get my answer?

 

[DaveC426913]

Do I multiply 93 x 10^(6) by 5.87 x 10^(12) to get my answer?

Where does the 93 x 10^6 come from in your thinking?

Take a step back and do a sanity check: what result are you being asked for? What results did you get? Did you answer what the question is asking?

 

[felizgu]

Where does the 93 x 10^6 come from in your thinking?

Take a step back and do a sanity check: what result are you being asked for? What results did you get? Did you answer what the question is

Given information:

- The speed of light is 186,000 miles per second.
- One light-year is the distance that light travels in one year (365 days).

I have to calculate the distance that light travels in one year.

Distance = Speed × Time

Distance = 186,000 miles per second × (365 days × 24 hours per day × 60 minutes per hour × 60 seconds per minute)

Distance = 5.88 × 10^12 miles

is this right?

If it is right, I say the number of miles in a light-year is 5.88 × 10^12 miles.

You say?

 

[DrClaude]

If it is right, I say the number of miles in a light-year is 5.88 × 10^12 miles.

That is correct.

Note however that a year is considered to be 365.25 days, not 365 (hence a leap year every four years). This does not change the numerical value of the length of the light year with 3 significant digits, as you wrote it.

 

[berkeman]

Distance = 186,000 miles per second × (365 days × 24 hours per day × 60 minutes per hour × 60 seconds per minute)

One tip that I learned in undergrad that has always helped me keep things straight in unit conversions is to use the trick of "multiply by 1" for each unit change. Multiplying a quantity by 1 does not change it, but it can be used to convert units if you make the 1 equal to a fraction involving the sets of units.

So I would write your equation above as:
$$Distance (miles) = \frac{186,000 miles}{second} \times {365 days} \times \frac{24 hours}{day} \times \frac{60 minutes}{hour} \times \frac{60 seconds}{minute}$$

You can see that the units on the RHS of the equation cancel out to give you the units of miles that you want on the LHS.

 

[felizgu]

One tip that I learned in undergrad that has always helped me keep things straight in unit conversions is to use the trick of "multiply by 1" for each unit change. Multiplying a quantity by 1 does not change it, but it can be used to convert units if you make the 1 equal to a fraction involving the sets of units.

So I would write your equation above as:
$$Distance (miles) = \frac{186,000 miles}{second} \times {365 days} \times \frac{24 hours}{day} \times \frac{60 minutes}{hour} \times \frac{60 seconds}{minute}$$

You can see that the units on the RHS of the equation cancel out to give you the units of miles that you want on the LHS.

1. Thank you for your reply.

2. I am not a college student. I graduated college in June 1994.

3. I am a middle-aged man conducting a self-study of mathematics.

 

[pbuk]

Please be aware that the 365 days in a year is an approximate number ... There is probably an official value certified by the ministry of unfathomable distances........

Close: it is actually the International Astronomical Union, and the official value is 365.25 days each of exactly 86,400 seconds.

https://www.iau.org/public/themes/measuring/

 

[felizgu]

Close: it is actually the International Astronomical Union, and the official value is 365.25 days each of exactly 86,400 seconds.

https://www.iau.org/public/themes/measuring/

Thanks for the link. However, I posted the numbers as given in the word problem.

 

[berkeman]

Thread is closed for moderation due to some issues with the OP not related to this thread.

 

[Mark44]

Thread closed due to OP being banned for creating multiple accounts.