# Units Conversion

We will typically measure distance in meters, time in seconds, and mass in kilograms. But not always.

In the lab, we might measure the speed of a cart as

## v = 12.3 m/s

But how fast is that? Really? I think of speed in miles per hour (mi/h or mph) or, at least in kilometers per hour (km/h). Quick, what's the "conversion factor" from meters per second to kilometers per hour?

Don't memorize conversion factors!

Just multiply by one.

## 2 = 2 [4/4] = 8/4

[4/4] is just one; that is [4/4] = 1. Likewise [km/1000 m] is one or [km/1000 m] = 1 and [60 s/min] is one or [60 s/min] = 1 and [60 min/h] is one or [60 min/h] = 1 . We can use these to change our velocity of v = 12.3 m/s to a velocity with units of km/h.

## v = 12.3 m/s [km/1000 m] [60 s/min] [60 min/h]

Notice that all the units "cancel" and we are left with km in the numerator and h in the denominator for km/h,

## v = 44.3 km/h

We can go ahead and even change this to a velocity in miles per hour, mi/h. We know that

so that means

## [ mi/1.61 km ] = 1

so we can can again "multiply by 'one'",

## v = 27.5 mi/h

Don't memorize conversion factors!

Just multiply by "one".