dimensional analysis

[Timorito]

hey guys does anyone know any good memory trick or something for dimensional analysis i have memeorized all the prefixes like nano is 10^-9 but i get really confused what goes where and if the 1 should be on the denomitor or numberator or the prefix. it really confuses me

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[Czarcasm]

hey guys does anyone know any good memory trick or something for dimensional analysis i have memeorized all the prefixes like nano is 10^-9 but i get really confused what goes where and if the 1 should be on the denomitor or numberator or the prefix. it really confuses me

I was following what you said... until you said that.

 

[Timorito]

like 1/grams or grams/1 ... i get confused when to do that... or 1/ nano nano/1 , hopefully you do now

 

[ashtonjam]

Each fraction should be a true statement. By that, I mean that you should be able to qualitatively say that the top and bottom are the same thing.

For example:

1) 1 kg = 1000 g. In a dimensional analysis, you could put 1 kg/1000 g OR 1000 g / 1 kg depending on what units you want to get in the end.

2) 1 mole = 6.02e23 molecules. In a stoichiometry problem, you could use 1 mol/6.02e23 molecules OR 6.02e23 molecules/1 mol. Sometimes you want your answers in molecules. Sometimes you want your answers to be in moles. You are allowed to flip fractions (true statements) to achieve your goals.

Example problem: How many nanometers are in 50 inches, if 1 in = 2.54 cm?

1 m = 10^9 nm. Don't put 1 m = 10^-9 nm! You should be thinking that there are a ton of nanometers in a meter, since nanometers are small. You want 10^9 nm in a meter, not 10^-9.

50 in * (2.54 cm/1 in) * (1 m/100 cm) * (10^9 nm/1 m) = your answer. This makes a lot more sense if you write this out on paper and cancel units as you go. Inches, centimeters, and meters should be paired up on top and bottom, nicely cancelling out. There is a 1 nm term on the top that does not cancel with anything; that is the correct unit for your answer.

 

[Czarcasm]

This is what I would do personally. If a certain equation is asking for units in meters, and you have an equation that has different units, here's how you can solve it (example):

Let's say you have:

5 cm x 10 Mm
-------------------
5 nm


Immediately convert the units to meters:

(5x10^-2m) x (1x10^7m)
--------------------------------------
(5x10^-9m)


Simplify the numerator by multiplying (remembering that exponents are the SUM when multiplying). In other words, you add them up: (-2) + 7 = 5. Therefore:

(5x10^5m)
----------------
(5x10^-9m)

At this point you can do one of two things. If working with exponents in the denominator makes you uncomfortable, turn it into a fraction.

1x10^-9 is the equivalent of: 1/10^9

5x10^5m
-------------
5 x (1/10^9m)


Because a fraction is in the denominator, it's the equivalent of writing it like this (multiplying the reciprocal):

5x10^5m x 1x10^9mm
-------------------------
5


And again, you multiple the numerator out:

5x10^14m
----------------
5

And solve for your answer:

1x10^14m

Hope this helps!


Oh and here's one more really helpful tip. For those scientific notation problems, if you need to express 0.0005m into scientific notation and forget whether to make the exponent positive or negative, always tell yourself this: if the number is getting bigger, the exponent gets smaller and vice versa. Works like a charm! Therefore, 0.0005 = 5x10^-3m!

 

[Blueprint MCAT Tutor]

Can you maybe list two or three problems that you got wrong? Explain how you solved the problems?

The folks above are offering great general advice but you explain exactly what mistakes you've made you'll get more focused answers.