# 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).

NOTE:

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

EXAMPLE:

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

OUTCOME:

Convert from one set of units to another

TEST YOURSELF!

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.

DEFINITION:

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).

NOTE:

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 cm^{3} is often called a liter (for
convenience).

EXAMPLE:

You may recall from physics:

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

Do these units match?

DEFINITION:

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).

OUTCOME:

Convert from one set of units to another

TEST YOURSELF!

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