Question

120 mL = what L

Answer 1

Cynthia message me if you are here

Answer 2

Deriving this is one of my favorite derivations. I only will use exact legal values.

20 mL = how many english fluid ounces. We'll start with the gallon, 128 fluid ounces.

Legally, there are 231 cubic inches per gallon.

1 gal = 231 in^3

Now take the cube root of both sides, remembering the law of exponents, (a*b)^c = a^c * b^c. A cube root is an exponent of (1/3). Dimensional analysis is the theory that you can manipulate the [gal] and the [in] like they were algebraic unknowns.

1 cube_root_gallon = cube_root(231) * inches ` ` ` ` ` (1)

Now a cube root of a gallon is the length of a side of a cube with volume one gallon. Lets convert this inches to centimeters. Legally

` ` 2.54 cm = 1 inch

multiply this equation by 1/inch both sides to get

` ` 2.54 cm/inch = inch/inch

notice that the right side is equivalent to 1

` ` 2.54 cm/inch = 1

Not multiply this equivalent to 1 on the right hand side of equation (1) to get

1 cube_root_gallon = cube_root(231) * inches * 2.54 cm/inch

and cancel the "inch" dimension on the numerator and demonenator right hand side

1 cube_root_gallon = cube_root(231) * 2.54 cm

now cube both sides to get gallons again, remembering the law of exponents, that is each factor on the right is cubed as well


1 gallon = 231 * (2.54)^3 cm^3

Now working on the left hand side, 4 quarts = 1 gallon, so by a similar argument 1 = 4 quarts/gallon and multiplying this to the left hand side of the equation (since multiplying by 1 doesn't change the value)

1 gallon*4 quarts/gallon = 231 * (2.54)^3 cm^3

cancelling "gallon"

4 quarts = 231 * (2.54)^3 cm^3

and 2 pints = 1 quart, so 2 pints/quart = 1, multiplying and cancelling

4 * 2 pints = 231 * (2.54)^3 cm^3

and a pint is legally 16 fluid ounces, 1 pint = 16 fluid oz, thus 1 = 16 fluid oz / pint; multiplying this value of 1 on the left hand side won't change anything, then cancelling "pints"

4 * 2 * 16 fluid oz = 231 * (2.54)^3 cm^3

now multiply both sides by 20/(231 * (2.54)^3)

4 * 2 * 16 * 20 / (231 * 2.54^3 ) fluid oz = 20 cm^3

since 1 mL is exactly equivalent to 1 cm^3, our answer is on the left-hand-side. via good calculator