Question

There are 200 ounces in 6 liters. How many milliliter (ml) are in 6 liters? (How to do in dimensional analysis?)

Answer 1

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Answer:

  6000 mL

Step-by-step explanation:

The prefix "milli-" is an SI standard prefix meaning 1/1000. So, 1 mL = (1/1000)L.

When doing dimension changes, you always want to use scale factors that have a value of 1, which is to say the numerator is equal to the denominator. For converting liters to milliliters, the scale factor you want will have mL in the numerator and L in the denominator:

  (1 mL)/(1/1000 L)   or   (1000 mL)/(1 L)

To do your conversion, multiply your liter volume by this factor.

  $(6\text{ L})\times\dfrac{1000\text{ mL}}{1\text{ L}}=\dfrac{6\times1000\text{ mL \cdot L}}{1\text{ L}}=6000\text{ mL}$

6 liters is 6000 milliliters.

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You will notice that the dimensions "L" cancel, which is the point of the exercise.

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Additional comment

6 L is closer to 202.884 fluid ounces. The conversion factor is ...

  $\dfrac{128\text{ fl oz}}{231\text{ in}^3}\times\dfrac{1\text{ in}^3}{(0.254\text{ dm})^3}\times\dfrac{1\text{ dm}^3}{1\text{ L}}=\dfrac{128\text{ fl oz}}{3.785411784\text{ L}}\quad\text{exactly}$