What is the speed of light in miles per hour using dimensional analysis?

[jemjabella42]

The speed of light is 2.99792458 x 10^8 meters/second. What is this speed in miles per hour? (There are 1609 meters in one mile).

I used dimensional analysis to get here:(2.99792458 x 10^8 meters/second) * (1 mile /1609 meters) * (3600 seconds / 1 hour)

My question is, what do I do with this next stepy: (2.99792458 x 10^8)(3600)

For some reason, scientific notation throws me off completely. Do I just enter this into a calculator from here or can I simplify this further?

 

[Spinnor]

The speed of light is 2.99792458 x 10^8 meters/second. What is this speed in miles per hour? (There are 1609 meters in one mile).

I used dimensional analysis to get here:(2.99792458 x 10^8 meters/second) * (1 mile /1609 meters) * (3600 seconds / 1 hour)


...

You got it, just multiply everything out. As a check Google "speed of light miles per hour"

http://www.universetoday.com/38040/speed-of-light-in-mph/

 

[Pengwuino]

The speed of light is 2.99792458 x 10^8 meters/second. What is this speed in miles per hour? (There are 1609 meters in one mile).

I used dimensional analysis to get here:(2.99792458 x 10^8 meters/second) * (1 mile /1609 meters) * (3600 seconds / 1 hour)

My question is, what do I do with this next stepy: (2.99792458 x 10^8)(3600)

For some reason, scientific notation throws me off completely. Do I just enter this into a calculator from here or can I simplify this further?

You can but you're missing your miles to meters conversion.

 

[jemjabella42]

You can but you're missing your miles to meters conversion.

I didn't forget it in my notes.. I just forgot to type it out after simplifying. Basically, I'm stuck on what my next step should be from (2.99792458 x 10^8)(3600)/1609. Should I just type this into the calculator from here? Or is there additional simplification?

 

[Pengwuino]

I didn't forget it in my notes.. I just forgot to type it out after simplifying. Basically, I'm stuck on what my next step should be from (2.99792458 x 10^8)(3600)/1609. Should I just type this into the calculator from here? Or is there additional simplification?

You're pretty much set to go. You can take it a step further and write it fully in scientific notation as

${{(2.99792458 \times 10^{8} {{meters}\over{second}})(3.6 \times 10^3{{seconds}\over{hour}})}\over{1.609 \times 10^{3}{{meters}\over{mile}}}}$

It's good practice for when you have to multiple numbers that are in scientific notation but not at all necessary for this problem. The good thing about writing it like this is that you can clearly see your answer should be on the order $10^{8}$ or so (within 1 or 2 powers of 10). Depending on how good you are with your calculator, it's easy to get a power of 10 put in the wrong place and your answer will be way off and you wouldn't notice it if you skimped on the scientific notation.