I am studying dimensional analysis right now, and I get most of it, but I don't understand how to solve this problem: 5982 ox./pt=BLANK g/ml. I'm not sure how you do dimension analysis with units per units like this one. Thanks!!
The pt probably means "pint" but I have never heard of a mass unit called an ox. Are you sure you typed the problem correctly?
There is an Australian rugby player named Orford with nickname "Ox" who has a mass of 92 kg. I doubt if that is the unit being used here.
There are about 454 ml in a pint
Dimensional analysis is a useful tool for converting between different units of measurement. In this problem, you are given a conversion factor of 5982 ox. (ounces) per pt. (pint) and you need to find the equivalent value in g/ml (grams per milliliter).
To solve this problem using dimensional analysis, you can set up a conversion factor ratio. By using the given conversion factor, you can create an equation where the units cancel out to give you the desired units.
Let's break down the given conversion factor:
5982 ox./pt
To set up the conversion factor ratio, you need to write it in a fraction form, with the units you want to convert from (pt.) as the denominator and the units you want to convert to (g and ml) as the numerator:
5982 ox. g
--------- = --------
pt. ml
Now, since you are trying to convert from ounces (ox.) to grams (g) and from pints (pt.) to milliliters (ml), you need to know the conversion factors for each.
Conversion factor for ounces to grams:
1 ox. = 28.35 g
Conversion factor for pints to milliliters:
1 pt. = 473.18 ml
Now, let's substitute these conversion factors into the equation:
5982 ox. g 5982 ox. g
--------- = -------- x ------------ = ----------- x 28.35
pt. ml 1 pt. ml
Now, you can simplify and solve the equation:
5982 x 28.35 ox. x g = ? g/ml
169770.7 g = ? g/ml
To get the final answer in g/ml, you need to divide 169770.7 g by the conversion factor for milliliters:
169770.7 g
-------------- = 169770.7 g/ml
1 ml
Therefore, the equivalent value of 5982 ox./pt. in g/ml is approximately 169770.7 g/ml.
Remember, dimensional analysis is a methodical approach that allows you to convert between units by canceling out unwanted units using conversion factors. It's important to have the correct conversion factors and pay attention to the unit cancellation.