Unit Conversions for Mere Mortals
So, you are taking a college science course. Maybe it
is physics, maybe it is chemistry, maybe its a lab.
Either way, you always end up with these problems
that involve unit conversions. You think you have the
hang of it, but sometimes you make some mistakes.
Here is my explanation for converting units.
Convert units? Me? Why? I have google. Yes, that is
true, google (for the most part) does an excellent
job at unit conversions. But....I doubt your
instructor will let you use google on your test.
Don't you think you should have a good idea of how to
do it?
If Curly were here, he would say that unit conversions involve 1 thing. He would be correct (but he died because he ate bacon at every meal - you can't do that!). The one thing for unit conversion is multiplication by 1. What? Yes. Multiplication by 1.
The key thing to realize is that units are an important part of a number and we don't want to change what that number represents, just its units. Take for instance the number 5. Suppose I do the following:
What would I get? Let me pretend
I am a noob and work it out.
its the same thing as what I
started with. You might say "duh - you
multiplied by 2/2 which is one". And you would
be correct. What if I do the following:
Well, that will still be equal to
5 because 6/3 is still 2. In this case, I am
still multiplying 5 by 1. If you are ok with
this, then you are ready for a real unit
conversion.
First, suppose I measure the length of my desk and I get:
Note the the units are important.
If I measured the desk and got a value of just
55, that is meaningless. 55 what? 55 chickens?
55 gobstoppers? 55 golden gate bridges?
Nonetheless, suppose I want the length of the
desk in inches instead of cm? I only need to
multiply by "1" in this case, my "1" will be
created from a a fraction with 0.394 inches and
1 cm since 1 cm = 0.394 inches. That will give:
Notice that the cm canceled since
that unit was on the top and the bottom. Really,
you can consider the unit to be like a variable
(in essence it is).
But HEY! you may say - I have been doing this anyway. Why can't I just say "to convert cm to inches, multiply by 0.394". Yes, this is what happens, but not how it happens. With this way, it is easier to do all sorts of conversions. All you need to know is one relationship (like 1 cm = 0.394 inches - OR - 2.54 cm = 1 inch). Let me do a couple of useful examples:
Convert 3 feet per minute to meters per second:
You see, it is possible to do a series of conversions in a row. The key thing to remember is to multiply by fractions that have equivalent things in the top and bottom and make the units cancel (notice I multiplied by 0.305 m over 1 ft so the ft cancel).
Next example - (this one is tricky for many students): Convert 345 cm2 into m2:
I did this one wrong (sort of
wrong) on purpose. This is similar to the
mistake many students make. They say there is 1
m2 in 100 cm2. This just
is not the case. Here is a simulation of that:
This is a square that is 10
smaller squares by 10 smaller squares. Although
there are 10 small squares in one side, there
are 100 total small squares in this big square.
So, for the above problem, it really should be:
Last example:
How fast is 20 furlongs per fortnight in meters per second?
Solution: what in the world is a forlong? I know a fortnight is two weeks. Type the following in google:
20 furlongs per fortnight in m/s - Yes, google calculator is pretty cool, but it is not without its flaws - see this post.
Hopefully, you have increased your skill points in unit conversion.
UPDATE: if you find this interesting and useful, you might also find my book useful - Workingman's Algebra. The basic idea behind this book is to give a fresh approach to algebra for those that truly need it (like students in introductory physics or chemistry). My other post - Curly's Law of Algebra is also similar to the material covered in the book.
If Curly were here, he would say that unit conversions involve 1 thing. He would be correct (but he died because he ate bacon at every meal - you can't do that!). The one thing for unit conversion is multiplication by 1. What? Yes. Multiplication by 1.
The key thing to realize is that units are an important part of a number and we don't want to change what that number represents, just its units. Take for instance the number 5. Suppose I do the following:
What would I get? Let me pretend
I am a noob and work it out.
its the same thing as what I
started with. You might say "duh - you
multiplied by 2/2 which is one". And you would
be correct. What if I do the following:
Well, that will still be equal to
5 because 6/3 is still 2. In this case, I am
still multiplying 5 by 1. If you are ok with
this, then you are ready for a real unit
conversion.
First, suppose I measure the length of my desk and I get:
Note the the units are important.
If I measured the desk and got a value of just
55, that is meaningless. 55 what? 55 chickens?
55 gobstoppers? 55 golden gate bridges?
Nonetheless, suppose I want the length of the
desk in inches instead of cm? I only need to
multiply by "1" in this case, my "1" will be
created from a a fraction with 0.394 inches and
1 cm since 1 cm = 0.394 inches. That will give:
Notice that the cm canceled since
that unit was on the top and the bottom. Really,
you can consider the unit to be like a variable
(in essence it is).
But HEY! you may say - I have been doing this anyway. Why can't I just say "to convert cm to inches, multiply by 0.394". Yes, this is what happens, but not how it happens. With this way, it is easier to do all sorts of conversions. All you need to know is one relationship (like 1 cm = 0.394 inches - OR - 2.54 cm = 1 inch). Let me do a couple of useful examples:
Convert 3 feet per minute to meters per second:
You see, it is possible to do a series of conversions in a row. The key thing to remember is to multiply by fractions that have equivalent things in the top and bottom and make the units cancel (notice I multiplied by 0.305 m over 1 ft so the ft cancel).
Next example - (this one is tricky for many students): Convert 345 cm2 into m2:
I did this one wrong (sort of
wrong) on purpose. This is similar to the
mistake many students make. They say there is 1
m2 in 100 cm2. This just
is not the case. Here is a simulation of that:
This is a square that is 10
smaller squares by 10 smaller squares. Although
there are 10 small squares in one side, there
are 100 total small squares in this big square.
So, for the above problem, it really should be:
Last example:
How fast is 20 furlongs per fortnight in meters per second?
Solution: what in the world is a forlong? I know a fortnight is two weeks. Type the following in google:
20 furlongs per fortnight in m/s - Yes, google calculator is pretty cool, but it is not without its flaws - see this post.
Hopefully, you have increased your skill points in unit conversion.
UPDATE: if you find this interesting and useful, you might also find my book useful - Workingman's Algebra. The basic idea behind this book is to give a fresh approach to algebra for those that truly need it (like students in introductory physics or chemistry). My other post - Curly's Law of Algebra is also similar to the material covered in the book.
