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  • 1. I.E.S. MARÍA BELLIDO - BAILÉN BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA METRIC SYSTEM1. METRIC SYSTEMIn the past, every country and in some cases every region were using different units ofmeasurement. This diversity made the commercial relations between nations and communitiesvery difficult. In 1792, to resolve these difficulties, the Academy of Sciences in Paris proposedthe 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 metricsystem coexists with their traditional measurements.The metric system is a system of units in which the multiple and submultiples of a unit ofmeasurement are related by a multiple or submultiple of 10.The metric system is used principally for the following magnitudes: Length Mass Capacity Area VolumeThe units of time are not part of the metric system. They are related between themselves in amultiple or submultiple of 60. Time is a magnitude of the sexagesimal system.2. COMPLEX AND SIMPLE MEASUREMENTSComplex 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 measurementsConvert each of the units into the desired unit.EXAMPLE: Convert the following to cm: 12 km 5 dam 42 cm. 1
  • 2. Convert simple measurements to complex measurementsThere are two cases: 2. To convert to smaller units, multiplication is1. To convert to larger units, division is used. used.5,317 mm 2.325 km − 2 km = 0.325 · 1,000 = 325 2.325 km= 2 km 325 m3. UNITS OF LENGTHThe 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 1m 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 ordividing the unit by one followed by as many zeros as there are places between them on thetable above. 2
  • 3. EXAMPLES: 50 m cm In this case, multiply (because the m is greater than the cm) the unitby one followed by two zeros, since there are two places between both units. 50 · 100 = 5,000 cm 4,385 mm m In this case, divide (because the mm is smaller than the m) byone followed by three zeros, since there are three places between both units. 4385 : 1,000 = 4.385 mOther measurements of length are to measure very large distances, especially in:ASTRONOMYAstronomical Unit: 1 UA = 149,597,871 kmAn astronomical unit is the mean distance from the Earth to the Sun. It is used in the measurement of orbits andtrajectories inside the Solar system.Light-year: 1 light year ≈ 9,461,000,000,000 kmThe light-year is equal to the distance traveled by light in one average solar year. It is used in astronomy to measureextremely large distances.The light-year is approximately equal to:MICROSCOPIC MEASUREMENTSMicrometre or Micron: 1 μm = 0.000001 mIt is equivalent to one millionth of one part meter.Nanometer: 1nm = 0.000000001mEquivalent to a billionth of a meter. Used to measure ultraviolet radiation, infrared radiation and light.Angstrom: 1Å = 0.0000000001 mEqual to one ten-billionth of a meter (long short). It is the unit used primarily to express wavelengths, molecular andatomic distances.4. UNITS OF MASSThe 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 1g 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. 3
  • 4. EXAMPLES: 50 kg dg. In this case, multiply (because the kilogram is greater than the decigram) the unit byone followed by four zeros, since there are four places between both units. 50 kg · 10,000 = 500,000 dg 408 mg dg In this case, divide (because the milligram is smaller than the decigram) byone followed by two zeros, since there are two places between both units. 408 : 100 = 4.08 dgOther 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 CAPACITYThe 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 1l 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 cl2,587 cl l In this case, divide, (because the centilitre is smaller than the litre) the unit by onefollowed by two zeros, since there are two places between both. 2,587 : 100 = 25.87 l6. UNITS OF AREAThe fundamental unit for measuring area is the square meter, which is the area of a squarewhose sides measure 1 meter.There are also other units for measuring large and small quantities of area: 4
  • 5. square kilometer km2 1,000,000 m2square hectometer hm2 10,000 m2square decameter dam2 100 m2square meter m2 1 m2square decimeter dm2 0.01 m2square centimeter cm2 0.0001 m2square 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 ordividing 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 unitby one followed by four zeros, since there are two places between both units. 1.5 · 10,000 = 15,000 m215,000 mm2 m2 In this case, divide (because the mm2 is smaller than the m2) by one followed bysix zeros, since there are three places between both units. 15.000 : 1,000,000 = 0.015 m2Other 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 m²7. 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 m3hectometer cubic hm3 1,000,000m3decameter cubic dam3 1,000 m3cubic meter m3 1 m3cubic decimeter dm3 0.001 m3cubic centimeter cm3 0.000001 m3cubic millimeter mm3 0.000000001 m3 Note that each unit is 1,000 times larger than the previous. 5
  • 6. Therefore, the problem of converting units to other units becomes an issue of multiplying ordividing the unit by one followed by as many trios of zeros as there are places between them.1.36 Hm3 m3In this case, multiply (because the Hm3 is greater than the m3) the unit by one followed by sixzeros, since there are two places between both units.1.36 · 1,000,000 = 1,360,000 m315,000 mm3 cm3In 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 cm38. RELATIONSHIP BETWEEN UNITS OF CAPACITY, VOLUME AND MASS Capacity Volume Mass (of water) 1 kl 1 m³ 1t 1l 1 dm3 1 kg 1 ml 1 cm³ 1g9. ENGLISH SYSTEMUnits of Length Units of Capacity Units of Mass Units of AreaInch = 2.54 cm. Pint (UK) = 0.568 litres Ounce = 28.3 grams Acre = 4,047 m².Foot = 12 inches = Pint (U.S.) = 0.473 Pound = 454 grams30.48 cm. litresYard = 3 feet = 91.44 Barrel = 159 litrescm. 6