Dimensional Analysis

[Timorito]

Hello guys i haved helped with dimensional analysis before and still getting these wrong. I was told to always put 1 infront of the larger number but it works sometimes and sometimes it doesnt.

Lets say we know a micro = 10^-6 but in some conversions you dont put the negative and some you do. How do you know when to put negative or wheter it goes on the bottom. No tutorial has explained this to me. Thanks

---

Members don't see this ad.

 

[Odi]

The prefixes never change. Micro, mega, and nano, to name a few are always 10^-6, 10^6, and 10^-9 respectively.

If you are told you have a wavelength of 123 nano meters... just slap on the prefix 10^-9 to make it: 123 x 10^-9 meters. If you have 194 megatons of a material just slap on the prefix 10^6 to make it: 194 x 10^6 tons.

Simply put the designated prefix at the end of your number for a quick and easy conversion.

Save dimensional analysis for more complicated conversions like a centiliter to a deciliter type of thing.

 

[azor ahai]

I try to convert into SI units on the fly as I read a problem. For example, if I read something like 900nm I write 9e-7m. If I read 200g, I write 1/5kg. If I read [H+] = 3e-10, I write pH = 10-log3 or 9.52.

If it is the most time-consuming part of the test for you (as it is with me), definitely practice it as much as possible.

 

[sazerac]

The whole point of conversion factors is that the numerator and the denominator are the same amount.

If you want to convert 2 meters to micrometers, start with 2 meters and multiply by the following conversion factor:
(10^6 micrometers / 1 meter)
This should intuitively make sense... in your gut you know micros are really small, and it's going to take a lot of them to make one meter.

You could have used this conversion factor instead:
(1 micrometer / 10^-6 meters)
this also makes intuitive sense, but negative exponents are yucky.

 

[sazerac]

Eventually after creating conversion factors like this for a month or so, you can start doing ninja-level conversion factors. Let's take converting from kilometers to meters as an example.

(1000 meter / 1 kilometer)

Take a look at that conversion factor again. You can cancel the meters on the numerator and the denominator, and are left with the conversion factor

(1000 / k)

That is a legitimate conversion factor! The letter "k" is 1,000. So the numerator and denominator are the same.

(k / 1000)

is also a conversion factor.

Here are some more:
1000m
1 / 1000m
100c
1 / 100c
10^6u
1 / 10^6 u
10^9n
1 / 10^9 n

Let's take an example. Convert 0.5m to cm.

0.5m (100c) = 50cm

Another: convert 5km into meters.

5km (1000 / k) = 5000m
("cancel the 'k' ")


This second post of mine might not make much sense right now. Don't worry. Go reread my first post, above, and use it to build proper conversion factors for all your questions. After the umpteenth time you convert meters to millimeters, liters to milliliters, and convert moles to millimoles, come back to this post and it will make sense that the underlying conversion factor was stuffing (1000m) into the denominator in each case.