## Thursday, March 14, 2013

### Jugs of water inside a liter.

Question:  A person has two glasses of water.  One has 130 milliliters in it.  The other has 6 centiliters in it.  What is the total amount of water in milliliters?  What is the total amount of water in centiliters?    The water in both glasses is poured into a one-liter jug.  What percent of the jug is empty?

Answer:  A milliliter is one-thousandth of a liter.  A centiliter is one-hundredth of a liter.  There are 10 milliliters in a centiliter so 6 centiliters is the same as 60 milliliters.   The total amount of water in the two jugs in milliliters is 130+60 =190.

190 milliliters is the same as 19.0 centiliters because there are 10 milliliters in each centiliter.

There are 1000 milliliters in the jug but only 190 milliliters of water.  This means 81.0% 100x(1-0.190) of the jug is empty.

Background:  The basic units of measures in the metric system are meter for distance, liter for volume and gram for weight.   A larger or small metric measure is created by adding a prefix to the basic unit.  For example, a kilometer is 1,000 meters and a millimeter is one thousandth of a meter.  Since there are 1,000 millimeters in a meter and 100 centimeters in a meter there must be 10 millimeters in a centiliter.

The chart below defines how placing a prefix in front of a basic unit changes the item being measured.

 Prefix Comparison to Basic Unit Kilo 1,000 Hecto 100 Deka 10 Basic Unit (Meter, Liter, or Gram) 1 Deci 1/10 Centi 1/100 Milli 1/1,000

Khan academy has several excellent videos describing how to convert one metric unit to another.  A link to my post describing two of the Khan videos is below.