Friday, March 15, 2013

Additional metric system problems.


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

Facts that can be gleaned from this chart:

·      A kilometer is one thousand meters.

·      A milliliter is one thousandth of a liter

·      A dekagram is ten grams.

·      A hectometer is one hundred kilometers.



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


Use this chart to solve the following problems:

How many milliliters are in 3.2 hectoliters?

How many centimeters are in a kilometer?

What is the name of the track event that consists of running one kilometer and 500 meters?

A box has 1 kilogram of a substance.    One person takes 2 hectograms.  A second person takes 4 dekagrams.   How much of the substance is left?

A box has 10 dekagrams of a substance.  Factory workers will put the substance in boxes that hold 5 decimeters?  How many boxes can the factory workers fill with the available material if there is no spillage?


Answers:

How many millimeters are in 3.2 hectoliters?


·      A liter has 1,000 thousand milliliters.   A hectoliter has 100 liters.  There are 100,000 (1,000x100) milliliters in a hectoliter.  3.2 hectoliters is the same as 320,000 milliliters (100,000 x 3.2).

How many centimeters in a kilometer?

·      There are 100 centimeters in a meter and 1,000 meters in a kilometer.   Multiply and get 100,000 centimeters in a kilometer.

What is the name of the track event that consists of running one kilometer and 500 meters?

·      A kilometer is 1,000 meters.  1,000 meters plus 500 meters is 1500 meters.   The event is called the fifteen hundred.


A box has 1 kilogram of a substance.    One person takes 2 hectograms.  A second person takes 4 dekagrams.   How much of the substance is left?

·      One kilogram is 1,000 grams. Two hectograms weigh 200 grams.  4 dekagrams is 40 grams.  The box with (1000-200-40) grams weighs 760 grams. 

A box has 10 dekagrams of a substance.  Factory workers will put the substance in boxes that hold 5 decimeters?  How many boxes can the factory workers fill with the available material if there is no spillage?

·      10 dekagrams is 100 grams.  5 decimeters is 0.5 grams.  The workers can fill 200 boxes.  


Also see tips section.

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