APROXIMACION NUMERICA

Marcela F. Garzón T.Ing. Petróleos

SIGNIFICANT FIGURES

• It’s considered that significant numbers are those numbers that have real meaning or provide meaning. The significant figures of a number are determined by its error. These are significant figures those wo occupy a position equal to or above the order or position of the error.

SIGNIFICANT FIGURES

• When expressed a number should be avoided if the use of sigificant figures, since it can be a source of confusion. The numbers should be rounded so that contain only significant figures

WHAT’S ROUNDING???

• Is called rouding to the process of elimination of insignificant figures.

EXAMPLE

• Consider a measure of length that gives a value of 5432.4764 m with an error of 0.8 m. The error is therefore the order of tenths of a meter. It is clear that all numbers that occupy a number less than the tenth position provide no information. Indeed, what sense does it give the number to the nearest thousandths if we say that the error is about 1 meter?.

The correct rounded number is 5432.5

THE RULE IN THE ROUNDING ARE

• If the figure is ignored is less than 5, is eliminated

• If the figure is eliminated, it increases by one unit the digit retained

• When the digit removed is 5, last figure is taken as the nearest eve number i.e. if the figure is even left on hold, and if it is odd, take the higher figure

RULES OF OPERATIONS WITH SIGNIFICANT FIGURES

• Rule 1: The experimental results are expressed with only a dubious figure, and with ± indicating uncertainty in measurement.

• Rule 2: The significant figures are counted from left to right, from the first nonzero digit digit and even doubtful.

• Rule 3: When you add or subtract two decimal numbers, the number of decimal digits of the result is equal to the amount with the least number of them.Note: One case of particular interest is the subtraction. Let us quote the following example: 30.3475-30.3472 = 0.0003

Note that each of the quantities have six significant figures and the result has only one. Subtracting significant figures are lost. This is important to keep in mind when working with calculators or computers where figures are to join and be subtracted.

First there should be additions and subtractions then to lose the least possible number of significant figures.

RULES OF OPERATIONS WITH SIGNIFICANT FIGURES

• Rule 4: When you multiply or divide two numbers, the number of significant figures in the result is equal to the factor with fewer numbers.

RULES OF OPERATIONS WITH SIGNIFICANT FIGURES

EXACTITUD Y PRECISION

• Exactitude refers to how close it is measured or calculated value of the true value. Precision refers to how close an individual value is measured or calculated with respect to other

EXACTITUDE

• La exactitude of a measurement refers to its proximity to the value it purports to measure.

PRECISION

• Is related to the number of decimal places used to express the measured, whereas numerical methods are iterative techniques, expresses how close an approximation or an estimate value with respect to approximations or previous iterations of the same

BIBLIOGRAPHY

• http://es.wikipedia.org/wiki/Cifras_significativas

• http://wapedia.mobi/es/Cifras_significativas

• http://es.wikiwix.com/?lang=es&action=Dígitos%20significativos

• http://www.mitecnologico.com/Main/ConceptosBasicosMetodosNumericosCifraSignificativaPrecisionExactitudIncertidumbreYSesgo

• http://html.rincondelvago.com/metodos-numericos_5.html

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