EC: Convert from one set of units to another

Converting units

System of units: SI units

Units are quite helpful:

What does "three rivers stadium is 4 away" mean? 4 what!?

Standardized units are more helpful:

"Three rivers stadium is 4 miles away" is more helpful than "three rivers is 15 lengths of my backyard away"

SI units are an international standard group of units based on the meter (length), second (time), kilogram (mass), degree Kelvin (temperature), ampere (current), lumen (light intensity), and mole (number of elementary entities).


The dimensions of each of the SI units is shown in parenthesis.

Other conventions: English units, CGS units

We will (primarily) use SI, but be familiar with others...

What units to use?

Use any that you like (but be consistent!).

You can (easily) convert them anyway! (see above)

Unit Conversions

Units with same dimensions -> easily inter-converted


$15\; steps = 25\; feet$ $\rightarrow$ $\frac{15\; steps}{25\; feet} = 1$


Convert from one set of units to another


So, if it is 1000 feet between Benedum and the Cathedral

$1000\; feet \left (\frac{15\; steps}{25\; feet} \right ) = 600\; steps$

If there are 3.2808 feet in a meter, how many meters is one step?

Multiple and compound units

How old are you? 600,000,000 seconds!? Saying 19 years is a lot easier or you could just say 600 Megaseconds.


Multiple units are units devised purely for convenience. They can be of two types: new names (1 hour is 3600 seconds), or prefixed units (1000 millimeters is 1 meter).


The dimensions of multiple units must be the same as the base unit (hours and seconds and days, etc. are all time units).

What units do you use for velocity, volume, pressure?

Treat units algebraicly -> moving 1 mile every 2 hours means:

$\left ( \frac{1\; mile}{2\; hours} \right ) = 0.5\; miles/hour$

Your container is 10 cm wide, 10 cm long, and 10 cm high. The volume is:

$(10cm)(10cm)(10cm) = 1000cm^3$

1000 cm3 is often called a liter (for convenience).


You may recall from physics:

$v(m/s) = v_o(m/s) + a(m/s^2)t(s)$

Do these units match?


Compound units are units made up through algabraic combination of base units. They are often given special names for convenience (volume: liter; force: Newton (pound); pressure: Pascal).


Convert from one set of units to another


Can you convert compound units? Let's give it a shot!