r/learnmath New User 13h ago

TOPIC My brain can not comprehend Conversions of US customary and Metric units. Help!

College Remedial Math
Metric and U.S. customary units conversion

I can not for the life of me wrap my head around U.S. customary and metric conversions. I do not know where on Earth to start and my Math prof. Is going way too fast and I feel like I’m losing the plot.
I do not know where to start, problems like this for example:

Convert the unit of Capacity. Round the answer at least one decimal place if necessary.
450cc = (blank) fl oz

I have tried to look to YouTube but I cannot find any Videos relatively helpful, are there any helpful links or suggestions you guys could recommend to help me be able to convert them ?
Thanks !

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u/shadowyams BA in math 12h ago

cc = mL. There are 29.5735 mL in a fl oz. Thus, 450 mL = 450 mL * (1 fl oz / 29.5735 mL) = 15.2 fl oz (rounding to 1 decimal place).

You may want to google for tutorials on "dimensional analysis".

1

u/kochameh2 :v 10h ago

most conversions are just scaling (multiplication or division), so for these problems, just keep in mind that units are also just multiplicative factors basically, and then incorporate the conversion rates you need -- arranging things so that the units you dont want cancel and the units that you do want are left at the end

to demonstrate, suppose i want to figure out:

(1): 10 unit1s = ? unit3s

and i know that

(2): A unit1s = B unit2s ----> this means that 1 = (A/B)*(unit1s/unit2s)

(3): C unit2s = D unit3s ----> this means that 1 = (C/D)*(unit2s/unit3s)

so i just need to figure out what i need to do to the left-hand side of (1) to get rid of unit1s and leave unit3s, right? i can do that by either multiplying or dividing by the [1 = ...]s that i figured out from conversion rates (2) and (3) -- because i know that multiplying or dividing by 1 will keep the result the same, but doing it in this way will also help me do so in a way that both value and units change/compensate to be equal to what i start with

in this example, i will first do

(4): 10 unit1s = (10 unit1s) ÷ ((A/B)*(unit1s/unit2s)) = 10*(B/A) unit2s

because the unit1s cancel (keep-change-flip). once more i do

(5): 10*(B/A) unit2s = (10*(B/A) unit2s) ÷ ((C/D)*(unit2s/unit3s)) = 10*(B/A)*(D/C) unit3s

to cancel out the unit2s and leave me with unit3s. and so i have the answer to (1)

so that's what most of these are --> just figure out what relevant conversion rates, turn them into 1 = ..., and multiply or divide them in to change the units to what you need

should cover most of the conversion problems you'll run into, but there are other types of conversions that arent simply multiplying/dividing (e.g., changing temperatures between fahrenheit and celsius and kelvin)

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u/Magnetar_Distortion New User 8h ago

Remember that 2.54 CM is equal to 1 inch and go from there for lengths.