# Math Help - Converting Units

1. ## Converting Units

Me again

How do I convert the following units

2. Originally Posted by moolimanj
Me again

How do I convert the following units
To convert units, treat the units as variables, and use a "conversion factor" to cancel out the old units. For example:

$18\text{ in} = 18\text{ in}\left(\frac11\right) = 18\text{ in}\left(\frac{1\text{ ft}}{12\text{ in}}\right)$

$= \frac{18\text{ in}\cdot\text{ft}}{12\text{ in}} = \frac{18}{12}\cdot\frac{\text{in}\cdot\text{ft}}{\ text{in}} = \frac32\cdot\frac{\not\text{in}\cdot\text{ft}}{\no t\text{in}} = \frac32\text{ ft}$

Similarly, for number 2:

$1\frac{\text{BTU}\cdot\text{in}}{^\circ\text{F}\cd ot\text{ft}^2\cdot\text{hr}}$

$= 1\frac{\text{BTU}\cdot\text{in}}{^\circ\text{F}\cd ot\text{ft}^2\cdot\text{hr}}
\left(\frac{1054.8\text{ J}}{1\text{ BTU}}\right)
\left(\frac{1\text{ W}\cdot\text{s}}{1\text{ J}}\right)
\left(\frac{1\text{ ft}}{12\text{ in}}\right)^2
\left(\frac{1\text{ in}}{0.0254\text{ m}}\right)
\left(\frac{9^\circ\text{F}}{5\text{ K}}\right)
\left(\frac{1\text{ hr}}{3600\text{ s}}\right)
$

And, as long as I didn't make a mistake in typing all of that, all of your units should cancel and you will be left with units of $\text{W}\text{m}^{-1}\text{K}^{-1}$. The other questions are fairly similar.

3. Thanks but I dont understand where the 18 came from. Can you please explain. Also, for part b, why has 32 pounds per square inch been converted accrding to BTU?

Can you please explain with detailed working/wording?

Many thanks

4. Originally Posted by moolimanj
Thanks but I dont understand where the 18 came from. Can you please explain.
It was an example that I made up on the spot (convert 18 inches to feet) just to illustrate the basic process.

Originally Posted by moolimanj
Also, for part b, why has 32 pounds per square inch been converted accrding to BTU?
That work is actually for part (i) (when I said it was for the second part that was a typo; I apologize). The working for the second part is quite similar.