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 = 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

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

1 mi = 1.61 km

so that means

[ ^mi/_{1.61 km} ] = 1

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

v = 44.3 ^km/_h [ ^mi/_{1.61 km} ]

v = 27.5 ^mi/_h

Don't memorize conversion factors!

Just multiply by "one".

Dimensional Analysis			Order of Magnitude
Return to Table of Contents, Ch 1 Introduction

(c) 2005, Doug Davis; all rights reserved