METRIC DECIMAL SYSTEM

1. BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA
METRIC SYSTEM
1. METRIC SYSTEM
In the past, every country and in some cases every region were using different units of
measurement. This diversity made the commercial relations between nations and communities
very difficult. In 1792, to resolve these difficulties, the Academy of Sciences in Paris proposed
the metric system.
This system has been progressively adopted by all countries, with the exception of Burma,
Liberia, and the United States. In some countries, such as the United Kingdom the metric
system coexists with their traditional measurements.
The metric system is a system of units in which the multiple and submultiples of a unit of
measurement are related by a multiple or submultiple of 10.
The metric system is used principally for the following magnitudes:
Length Mass Capacity Area Volume
The units of time are not part of the metric system. They are related between themselves in a
multiple or submultiple of 60. Time is a magnitude of the sexagesimal system.
2. COMPLEX AND SIMPLE MEASUREMENTS
Complex measurements are expressed using different types of units:
3 kg 200 g 5 km 120 m.
Simple Measurements are expressed using only one type of unit:
3.2 kg 5.12 m.
Convert complex measurements to simple measurements
Convert each of the units into the desired unit.
EXAMPLE: Convert the following to cm: 12 km 5 dam 42 cm.
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2. Convert simple measurements to complex measurements
There are two cases:
1. To convert to larger units, division is used.
5,317 mm
2. To convert to smaller units, multiplication is
used.
2.325 km − 2 km = 0.325 · 1,000 = 325
2.325 km= 2 km 325 m
3. UNITS OF LENGTH
The fundemental unit for measuring length is the meter.
There are also other units for measuring large and small quantities, the most common are:
kilometer km 1,000 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
Note that each unit is 10 times larger than the previous.
Therefore, the problem of converting units to other units becomes an issue of multiplying or
dividing the unit by one followed by as many zeros as there are places between them on the
table above.
EXAMPLES: 50 m cm In this case, multiply (because the m is greater than the cm) the unit
by one followed by two zeros, since there are two places between both units. 50 · 100 = 5,000 cm
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3. 4,385 mm m In this case, divide (because the mm is smaller than the m) by
one followed by three zeros, since there are three places between both units. 4385 : 1,000 = 4.385 m
Other measurements of length are to measure very large distances, especially in:
ASTRONOMY
Astronomical Unit: 1 UA = 149,597,871 km
An astronomical unit is the mean distance from the Earth to the Sun. It is used in the measurement of orbits and
trajectories inside the Solar system.
Light-year: 1 light year ≈ 9,461,000,000,000 km
The light-year is equal to the distance traveled by light in one average solar year. It is used in astronomy to measure
extremely large distances.
The light-year is approximately equal to:
MICROSCOPIC MEASUREMENTS
Micrometre or Micron: 1 μm = 0.000001 m
It is equivalent to one millionth of one part meter.
Nanometer: 1nm = 0.000000001m
Equivalent to a billionth of a meter. Used to measure ultraviolet radiation, infrared radiation and light.
Angstrom: 1Å = 0.0000000001 m
Equal to one ten-billionth of a meter (long short). It is the unit used primarily to express wavelengths, molecular and
atomic distances.
4. UNITS OF MASS
The fundemental unit for measuring mass is the gram.
There are also other units for measuring large and small quantities, the most common are:
kilogram kg 1,000 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
Note that each unit is 10 times larger than the previous.
EXAMPLES: 50 kg dg. In this case, multiply (because the kilogram is greater than the decigram) the unit by
one followed by four zeros, since there are four places between both units. 50 kg · 10,000 = 500,000 dg
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4. 408 mg dg In this case, divide (because the milligram is smaller than the decigram) by
one followed by two zeros, since there are two places between both units. 408 : 100 = 4.08 dg
Other units of mass:
Metric ton or tonne
It is used to measure very large masses. 1 t = 1,000 kg
Quintal metric : 1 q = 100 kg
Example:
5. UNITS OF CAPACITY
The fundemental unit for measuring capacity is the litre or liter.
There are also other units for measuring large and small quantities, the most common are:
kiloliter kl 1,000 l
hectoliter hl 100 l
decaliter dal 10 l
liter l 1 l
deciliter dl 0.1 l
centiliter cl 0.01 l
mililiter ml 0.001 l
Note that each unit is 10 times larger than the previous.
EXAMPLES: 50 hl cl In this case, multiply (because the hectolitre is greater than the centilitre)
the unit by one followed by four zeros, since there are four places between both. 50 · 10,000 = 500,000 cl
2,587 cl l In this case, divide, (because the centilitre is smaller than the litre) the unit by one
followed by two zeros, since there are two places between both. 2,587 : 100 = 25.87 l
6. UNITS OF AREA
The fundamental unit for measuring area is the square meter, which is the area of a square
whose sides measure 1 meter.
There are also other units for measuring large and small quantities of area:
square kilometer km2
1,000,000 m2
square hectometer hm2
10,000 m2
square decameter dam2
100 m2
square meter m2
1 m2
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5. square decimeter dm2
0.01 m2
square centimeter cm2
0.0001 m2
square milimeter mm2
0.000001 m2
Note that each unit is 100 times larger than the previous.
Therefore, the problem of converting units to other units becomes an issue of multiplying or
dividing the unit by one followed by as many pairs of zeros as there are places between them.
EXAMPLES: 1.5 hm2
m2
In this case, multiply (because the hm2
is greater than the m2
) the unit
by one followed by four zeros, since there are two places between both units. 1.5 · 10,000 = 15,000 m2
15,000 mm2
m2
In this case, divide (because the mm2
is smaller than the m2
) by one followed by
six zeros, since there are three places between both units. 15.000 : 1,000,000 = 0.015 m2
Other units of land area measurements:
Hectare is equivalent to the square hectometer.
1 ha = 1 hm2
= 10,000 m²
Are is equivalent to the square decameter.
1 a = 1 dam2
= 100 m²
7. UNITS OF VOLUME
The fundamental unit for measuring volume is the cubic meter.
There are also other units for measuring large and small quantities of volume:
cubic kilometer km3
1,000,000,000 m3
hectometer cubic hm3
1,000,000m3
decameter cubic dam3
1,000 m3
cubic meter m3
1 m3
cubic decimeter dm3
0.001 m3
cubic centimeter cm3
0.000001 m3
cubic millimeter mm3
0.000000001 m3
Note that each unit is 1,000 times larger than the previous.
Therefore, the problem of converting units to other units becomes an issue of multiplying or
dividing the unit by one followed by as many trios of zeros as there are places between them.
1.36 Hm3
m3
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6. In this case, multiply (because the Hm3
is greater than the m3
) the unit by one followed by six
zeros, since there are two places between both units.
1.36 · 1,000,000 = 1,360,000 m3
15,000 mm3
cm3
In this case, divide (because the mm3
is smaller than the cm3
) by one followed by three zeros,
since there is one place between both units.
15,000 : 1,000 = 15 cm3
8. RELATIONSHIP BETWEEN UNITS OF CAPACITY, VOLUME AND MASS
Capacity Volume Mass (of water)
1 kl 1 m³ 1 t
1 l 1 dm3
1 kg
1 ml 1 cm³ 1 g
9. ENGLISH SYSTEM
Units of Length Units of Capacity Units of Mass Units of Area
Inch = 2.54 cm.
Foot = 12 inches =
30.48 cm.
Yard = 3 feet = 91.44
cm.
Pint (UK) = 0.568 litres
Pint (U.S.) = 0.473
litres
Barrel = 159 litres
Ounce = 28.3 grams
Pound = 454 grams
Acre = 4,047 m².
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7. In this case, multiply (because the Hm3
is greater than the m3
) the unit by one followed by six
zeros, since there are two places between both units.
1.36 · 1,000,000 = 1,360,000 m3
15,000 mm3
cm3
In this case, divide (because the mm3
is smaller than the cm3
) by one followed by three zeros,
since there is one place between both units.
15,000 : 1,000 = 15 cm3
8. RELATIONSHIP BETWEEN UNITS OF CAPACITY, VOLUME AND MASS
Capacity Volume Mass (of water)
1 kl 1 m³ 1 t
1 l 1 dm3
1 kg
1 ml 1 cm³ 1 g
9. ENGLISH SYSTEM
Units of Length Units of Capacity Units of Mass Units of Area
Inch = 2.54 cm.
Foot = 12 inches =
30.48 cm.
Yard = 3 feet = 91.44
cm.
Pint (UK) = 0.568 litres
Pint (U.S.) = 0.473
litres
Barrel = 159 litres
Ounce = 28.3 grams
Pound = 454 grams
Acre = 4,047 m².
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