Basic Math/need help

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Question
how many grams = one pound?
how many milliters = one microgram?
how many milliters = one gram?
how many milliters = one milligram?
how many milliters = one unit?
how many grams = one ounce?
how many milliters = one pound?
how many milligrams = one grain?
how many milligrams = one dram?
how many drams = one millileter?


Answer
You are talking about 4 different measuring systems here:
U.S. and metric volume measures and
U.S. and metric mass (weight) measures.

Let's list what we know about each first:
 In U.S. volume units the Gallon is defined as
 EXACTLY 231 cubic inches,
I gallon is also subdivided into:
4 quarts
8 pints
16 cups
128 fluid ounces
256 tablespoons
768 teaspoons
1,024 fluid drams
and 46,080 drops.

The metric units for volume are:
1 liter defined as 1 cubic decimeter
and 1,000 milliliters = 1 liter

From this we can find connections to the U.S. units because 1 inch is EXACTLY 0.254 decimeters.
cubing both we get 1 cubic inch = 0.0163871 cubic decimeters.
So now 1 gallon = 231 cubic inches
               = 3.78542 cubic decimeters or liters
               = 3,785.42 milliliters
So then 1 fluid ounce = 29.57359 milliliters

The unit call "unit" is used to measure the ethanol content in drinks and is defined as 10 milliliters of of the alcohol.

So here are the answers to the volume to volume questions:
10 milliliters of alcohol = 1 unit
0.2705116 fluid drams = 1 milliliter

Now for the U.S. (avoirdupois) mass measures:
1 pound = 16 ounces
       = 256 drams
       = 7,000 grains

The metric mass measures are:
1 kilogram = 1,000 grams
1 gram     = 1,000 milligrams
          = 1,000,000 micrograms

The connection between the two is defined as
EXACTLY 453.59237 grams = 1 pound

Now we can answer the 4 mass to mass questions:
453.59237 grams = 1 pound
28.349523 grams = 1 ounce
4.05 milligrams = 1 grain
110.74 milligrams = 1 dram

There are 4 more questions about metric volume to U.S. mass, but these can not be done unless you know the density of the substance in question. Let's use water because it's density is exactly 1 gram of mass per milliliter of volume.

So here are the last 4 conversions using water:
0.000001 milliliters of water = 1 microgram
1 milliliter of water = 1 gram
0.001 milliliters of water = 1 milligram
28.349523 milliliters of water = 1 pound  

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Cullen Porter

Expertise

Any math question up to Algebra. I have finished Calculus, so I will try to answer these questions also.

Experience

I am presently a hotel engineer and I have done some computer programming in college.

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I am currently writing my first non-fiction work which I will have on my website soon. It is like the "Powers of Ten" video short that describes the large and the small limits of reality.

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A Bachelor's of Science degree.

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Semair on Quarks, technical drawings in high school drafting course.

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