I.E.S. MARÍA BELLIDO - BAILÉN

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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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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  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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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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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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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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