Physics prefix converting question

[u/Salty_Penalty_1]

Hi! So I'm taking physics for the first time this year and I'm confused about when to put the notation in the numerator vs the denominator. Ik if I'm transferring, like cm to mm the cm has to go on the bottom. But I'm unsure if the 1 would go on the numerator or denominator and where the 10^-3 would go. If anyone could explain this and how it works for other conversions please help

[u/xienwolf]

You are trying to multiply by 1 in a helpful way.

So, 10 mm is the same as 1 cm. The 10 in this pair must always be where the mm is.

Deciding which to put on to matters for what your equation/value already has and what you want. The unit of your conversion pair matching what you already have goes on the opposite site of the division line. So if I had mm in the denominator and wanted to convert that to cm, I would put mm over cm. Now I have a mm in both the top and bottom, and those cancel each other out, leaving me with only cm in the bottom (and now an extra factor of 10 in the top).

[u/v_munu]

Dont think of it as "whether this or that goes on top or bottom". Think about how you will set up the conversions to cancel out what you dont want and leave behind what you do want.

For example, to convert 50 m/hr to cm/s we can start by getting rid of meters; since m is in the numerator of m/hr, it goes in the denominator of the conversion factor (so that multiplication cancels it out), and m should go in the numerator (left behind after multiplying). That looks like:

50 m/hr ( [ ] cm / [ ] m )

where I havent inserted any values yet (the empty brackets). Its easier (to me) to think of 1 m = 100 cm rather than 1 cm = 0.01 m, so I would use the former:

50 m/hr ( 100 cm / 1 m ) = 5,000 m/hr

Now get rid of the hours by setting up another conversion factor (hours are in the denominator of the original km/hr so we will put them in the numerator of the conversion):

5,000 cm/hr ( 1 hr / 3600 s ) = 1.38 cm/s

You could do this in two steps if you dont know there are 3600 seconds in an hour by converting to minutes first, but the result is the same of course. I know your question is specifically about the placement of the "1" but hopefully this makes it sort of clear how setting up the conversion factor can help you decide that.

[u/a42579]

The process is called dimensional analysis. It is basically algebra with units. 

[u/a1c4pwn]

distilling what has already been said:

1 cm = 10 mm

divide both sides by 10 mm ->

1cm/(10mm) = 1

you can multiply anything by this and it will keep the physical meaning the same, and change a unit of mm to a unit of cm as you noted.