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Calculeu la diagonal d'un rectangle de costats 10 i 4 cm.  Dóna el resultat arrodonit a dues xifres decimals.

Si considerem com resultat exacte el que has obtingut en l'apartat anterior, i com valor aproximat 11 cm, quin error absolut i quin error relatiu s'ha comés en aquesta aproximació?

Usant el Teorema de Pitàgoras, amb les dades  a= 10 cm i b=4 cm

d squared equals a squared plus b squared d squared equals 10 squared plus 4 squared d squared equals 100 plus 16 d squared equals 116 d equals square root of 116 equals 10 comma 77 space c m

Ara considerem d= 10,77 cm valor exacte  i considerem  d'=11 cm com valor aproximat de la diagonal

e r r o r space a b s o l u t space equals space divided by v a l o r space e x a c t e minus v a l o r space a p r o x i m a t divided by space equals space divided by 10 comma 77 minus 11 divided by space equals space divided by negative 0 comma 23 divided by space equals space 0 comma 23 space c m e r r o r space r e l a t i u space equals space fraction numerator e r r o r space a b s o l u t over denominator divided by v a l o r space e x a c t e divided by end fraction equals fraction numerator divided by v a l o r space e x a c t e minus v a l o r space a p r o x i m a t divided by over denominator divided by v a l o r space e x a c t e divided by end fraction equals space fraction numerator 0 comma 23 over denominator 10 comma 77 end fraction equals 0 comma 02135 rightwards double arrow 2 comma 13 percent sign

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