# What is the correct way to conver 14,28 m/s to mph and why does the decimal relocate?

1. Aug 8, 2012

### Sqw

This is not a homework question, but it is from a book....

In a nuclear chemistry experiment, an alpha particle is found to have a velocity of 14,285 m/s. Convert this measurement into miles/hour.

I want to verify the correct way to do this, and I also have a question about the decimal point relocating.

What I did (first):

14,285 meters per second * 3600 seconds in an hour = 51426000

51426000 / 1609.344 meters per mile = 31961.467 mph

The book says the right answer is: 8.2796 x 10^10

However, when I google " 14,285 meters per second to miles per hour," Google's converter agrees with me...

But if I do:

14,285 meters * 1 mile * 60 sec * 60 min / 0.000621371 * 1 sec * 1 min

I get 82762150148.62296438 Which is almost the same as the book. Except the book has the decimal between the 8 and the 2 and gets 8.2796 instead of 8.2762 which I presume is because they're omitting insignificant numbers during calculation, but I still don't understand how the decimal got moved between the 8 and the 2 while mine is in middle....

My questions are:

Which way is correct to convert this?

And also, more importantly, why does the book move the decimal between the 8 and the 2?

2. Aug 8, 2012

### Simon Bridge

Re: What is the correct way to conver 14,28 m/s to mph and why does the decimal reloc

miles per hour??

That seems awfully fast doesn't it? Reality check - what is the speed of light in mph?

Note: the book moves the dp because it is using standard scientific notation.
So 2224 (standard form) = 2.224x103 (scientific notation)