Decimal metric system: length, mass, capacity, surface and volume

To make measurements, you need a system of units, that is, a set of magnitudes with which to compare those things that you want to measure.

The decimal metric system is a system of units in which the multiples and sub-multiples of the unit of measurement are interrelated by multiples or sub-multiples of 10.

For example, the following belong to metric units: gram and kilogram (to measure the mass), meter and centimeter (for measuring length) or liter (to measure capacity).

Apart from the metric system, there are other systems of units: the Anglo-Saxon system, the so-called traditional measurements, etc.

Measurements of length

The unit for measuring length is the meter. However, there are other units:

Name Symbol Equivalence
kilometer km 1000 m
hectometer hm 100 m
decameter dam 10 m
meter m 1 m
decimeter dm 0.1 m
centimeter cm 0.01 m
millimeter mm 0.001 m

To convert an amount from one unit into another:

  • If the original unit is less than the one we want to get, the amount will be divided by 10 as many times as the number of rows that have to be “climbed” in the table above.
  • If the original unit is larger than the one we want to get, the amount will be multiplied by 10 as many times as the number of rows that have to be “gone down” in the table above.

Example

If you want to convert 1400 meters into decameters: One meter is less than a decameter therefore we have to divide 1400 by 10 once (because we have to go up once from the meter to decameter)

140010=140 decameters

That is, 1400 meters are 140 decameters.

Measurements of mass

The unit for measuring mass is the gram. The other units that exist are:

Name Symbol Equivalence
kilogram kg 1000 g
hectogram hg 100 g
decagram dag 10 g
gram g 1 g
decigram dg 0.1 g
centigram cg 0.01 g
milligram mg 0.001 g

To convert an amount from one unit into another one:

  • If the original unit is less than the one we want to get, the amount will be divided by 10 as many times as the rows that have to be "climbed" in the table above.
  • If the original unit is larger than the one we want to get, the amount will be multiplied by 10 as many times as the rows that have to be "gone down" in the table above.

Example

If we want to convert 23,4 hectograms into decigrams:

An hectogram is greater than a decigram, therefore we have to multiply 23,4 by 10 three times given that in the above table we have to move down three rows to go from hectograms to decigrams.

Therefore:

23,4⋅10⋅10⋅10=23.400 decigrams.

Namely, 23,4 hectograms are 23.400 decigrams.

Measurements of capacity

To measure capacity the unit used is the liter. The following table shows other common measurements of capacity:

Name Symbol Equivalence
kiloliter kl 1000 l
hectoliter hl 100 l
decaliter dal 10 l
liter l 1 l
deciliter dl 0.1 l
centiliter cl 0.01 l
milliliter ml 0.001 l

To convert a number from one unit to another:

  • If the original unit is less than the one we want to get, the amount will be divided by 10 the same number of times as the number of rows that have to be “climbed” in the table above.
  • If the original unit is larger than the one we want to get, the amount will be multiplied by 10 the same number of times as the number of rows that have to be “gone down” in the table above.

Example

If you want to convert 400 milliliters to liters:

If we go from milliliters to liters we have to go up three rows, then we must divide by 10 three times (which is the same as dividing by 1000). Therefore:

400:1000=0,4 liters.

Namely 400 milliliters are 0,4 liters.

Measurements of surface

To measure surfaces, the basic unit is the square meter, although the following units are also used:

Name Symbol Equivalence
square kilometer km2 1.000.000 m2
square hectometer hm2 10.000 m2
square decameter dam2 100 m2
square meter m2 1 m2
square decimeter dm2 0.01 m2
square centimeter cm2 0.0001 m2
square millimeter mm2 0.000001 m2

To switch a number from one unit to another:

  • If the original unit is less than the one we want to get, the amount will be divided by 100 the same number of times as the number of rows that have to be “climbed” in the table above.
  • If the original unit is larger than the one we want to get, the amount will be multiplied by 100 the same number of times as the number of rows that have to be “gone down” in the table above.

Example

If you want to convert 0,003 square kilometers to square decameters, then, in order to pass from square kilometers to square decametres, we move down two rows in the table above, therefore we must multiply by 100 twice (or what is the same, per 10.000) . Therefore:

0,003⋅10000=30 square decameters.

Namely, 0,003 square kilometers are 30 square decameters.

Measurements of volume

The most commonly used unit for measuring volume is the cubic meter. Other units commonly used are:

Name Symbol Equivalence
cubic kilometero km3 1.000.000.000 m3
cubic hectometer hm3 1.000.000 m3
cubic decameter dam3 1000 m3
cubic meter m3 1 m3
cubic decimeter dm3 0.001 m3
cubic centimeter cm3 0.000001 m3
cubic millimeter mm3 0.000000001 m3

To switch a number from one unit to another:

  • If the original unit is less than the one we want to get, the amount will be divided by 1000 the same number of times as the number of rows that have to be “climbed” in the table above.
  • If the original unit is larger than the one we want to get, the amount will be multiplied by 1000 the same number of times as the number of rows that have to be “gone down” in the table above.

Example

If you want to convert 6.000.000 cubic centimeters into cubic decimeters, you have to climb only one row, then it must divid it once by 1.000:

6.000.000:1.000=6.000 cubic decimeters.

Therefore 6.000.000 cubic centimeters are 6.000 cubic decimeters.