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Aproximaciones y error Ejercicio n 1.- Clasifica los siguientes nmeros como naturales, enteros, racionales, irracionales y/o reales: EMBED Equation.DSMT4 Solucin: EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 Ejercicio n 2.- EMBED Equation.DSMT4  Solucin:  Ejercicio n 3.- Sita cada nmero en la casilla correspondiente (recuerda que puede ir en ms de una): EMBED Equation.DSMT4  Solucin:  Ejercicio n 4.- Clasifica los siguientes nmeros como naturales, enteros, racionales, irracionales y/o reales: EMBED Equation.DSMT4 Solucin: EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 Ejercicio n 5.- Escribe en forma de intervalo y representa en cada caso: a) Nmeros comprendidos entre -1 y 4, ambos incluidos. b) Nmeros mayores que 0. c) Nmeros menores que -2 y el propio -2. d) Nmeros comprendidos entre 3 y 4, incluido el 4, pero no el 3. Solucin: a) [-1, 4]  b) (0, +)  c) (-, -2]  d) (3, 4]  Ejercicio n 6.- a) Escribe en forma de intervalo y representa: EMBED Equation.DSMT4 EMBED Equation.DSMT4 b) Escribe en forma de intervalo y representa: EMBED Equation.DSMT4 EMBED Equation.DSMT4 Solucin: EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Ejercicio n 7.- a) Escribe en forma de desigualdad y representa: EMBED Equation.DSMT4 EMBED Equation.DSMT4 b) Escribe en forma de intervalo y representa: EMBED Equation.DSMT4 EMBED Equation.DSMT4 Solucin: EMBED Equation.DSMT4  EMBED Equation.DSMT4  b) EMBED Equation.DSMT4  EMBED Equation.DSMT4  Ejercicio n 8.- a) Escribe en forma de intervalo y representa en cada caso: EMBED Equation.DSMT4 EMBED Equation.DSMT4 b) Escribe en forma de desigualdad y representa: EMBED Equation.DSMT4 EMBED Equation.DSMT4 Solucin: EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Ejercicio n 9.- Nos dicen que la medida de un campo de forma rectangular es de 45,236 m de largo por 38,54 m de ancho. Sin embargo, no estamos seguros de que las cifras decimales dadas sean correctas. a) Da una aproximacin (con un nmero entero de metros) para las medidas del largo y del ancho del campo. b) Da una cota para el error absoluto y otra para el error relativo cometidos al aproximar de esta forma. Solucin: a) Largo 45 m. Ancho 39 m. b) El error absoluto es menor que media unidad del orden de la ltima cifra significativa: Error absoluto < e Una cota para el error relativo es: EMBED Equation.DSMT4 Por tanto: Largo: |Error absoluto| < 0,5 m EMBED Equation.DSMT4 Ancho: |Error absoluto| < 0,5 m EMBED Equation.DSMT4 Ejercicio n 10.- a) Da una aproximacin, con tres cifras significativas, para cada una de las siguientes cantidades: I) 854 238 personas II) 3,1694 m III) 928 412 mg b) Cules son los errores absoluto y relativo cometidos en cada caso? Solucin: I) 854 238 personas 854 miles de personas Error absoluto = Valor real - Valor aproximado = 854 238 - 854 000 = 238 personas EMBED Equation.DSMT4 II) 3,1694 m 3,17 m Error absoluto = 3,1694 - 3,17 = - 0,0006 m EMBED Equation.DSMT4 III) 928 412 mg 928 miles de mg Error absoluto = 412 mg EMBED Equation.DSMT4 Ejercicio n 11.- En una librera se han vendido 5 PQbѼ{cQc81j L hzmCJOJQJUV^JaJmH sH "hzmCJOJQJ^JaJmH sH .hzm56CJOJQJ\]^JaJmH sH 1j L hzmCJOJQJUV^JaJmH sH "hzmCJOJQJ^JaJmH sH +jhzmCJOJQJU^JaJmH sH (hzm5CJOJQJ\^JaJmH sH 1hzm56>*CJOJQJ\]^JaJmH sH hzmmH sH hhzm5>*mH sH PQb 1 J K d e v w ^gdzm 0 gdzmgdzm$gdzm$a$gdzmdmm       - . / 0 1 2 F ӾӬ}ӾӬdN<Ӭ"hzmCJOJQJ^JaJmH sH +j hzmCJOJQJU^JaJmH sH 1j L hzmCJOJQJUV^JaJmH sH +jhzmCJOJQJU^JaJmH sH 1j L hzmCJOJQJUV^JaJmH sH "hzmCJOJQJ^JaJmH sH (hzm5CJOJQJ\^JaJmH sH +jhzmCJOJQJU^JaJmH sH +j[hzmCJOJQJU^JaJmH sH F G H I K L ` a b c d e s v w к}gR=R.hzm>*CJOJQJ^JaJ)h 56>*CJOJQJ\]^JaJ)hzm56>*CJOJQJ\]^JaJ+jhhzmCJOJQJU^JaJmH sH 1j L hzmCJOJQJUV^JaJmH sH "hzmCJOJQJ^JaJmH sH "hzmCJOJQJ^JaJmH sH +jhzmCJOJQJU^JaJmH sH +jhzmCJOJQJU^JaJmH sH 1j L hzmCJOJQJUV^JaJmH sH w x ʸp^V=((h 5CJOJQJ\^JaJmH sH 1h 56>*CJOJQJ\]^JaJmH sH hzmmH sH #j"hzmCJOJQJU^JaJ&hzm56CJOJQJ\]^JaJ hzm6CJOJQJ]^JaJ#jhzmCJOJQJU^JaJ hzm5CJOJQJ\^JaJ#j9hzmCJOJQJU^JaJ)j L hzmCJOJQJUV^JaJhzmCJOJQJ^JaJ#jhzmCJOJQJU^JaJ " # % & ' ( ) * + 5 6 8 9 J  2 T^Tgd gd $ 0 gd  0 gd    ! # $ % ' 4 5 6 7 9 J ׾閈pp[E0)h 56>*CJOJQJ\]^JaJ+jjh CJOJQJU^JaJmH sH (h 5CJOJQJ\^JaJmH sH .h 56CJOJQJ\]^JaJmH sH jh UmHnHu"h CJOJQJ^JaJmH sH +jfh CJOJQJU^JaJmH sH 1j L h CJOJQJUV^JaJmH sH "h CJOJQJ^JaJmH sH +jh CJOJQJU^JaJmH sH J Ϻݔq_J8#jzh CJOJQJU^JaJ)j, L h CJOJQJUV^JaJ#jwwh CJOJQJU^JaJ)j- L h CJOJQJUV^JaJh CJOJQJ^JaJ&h 56CJOJQJ\]^JaJ#j sh CJOJQJU^JaJ)j. 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Aproxima la cantidad obtenida dando dos cifras significativas. b) Di cul es el error absoluto y cul el error relativo cometidos al hacer la aproximacin. Solucin: a) 5 271 32,45 = 171 043,95 17 decenas de miles de b) Error absoluto = Valor real - Valor aproximado = 171 043,95 - 170 000 = 1 043,95 EMBED Equation.DSMT4 Ejercicio n 12.- a) Expresa con un nmero razonable de cifras significativas cada una de las siguientes cantidades: I) Asistentes a un concierto: 25 342 personas. II) Premio que dan en un concurso: 328 053 . III) Nmero de libros de cierta biblioteca: 52 243. b) Calcula el error absoluto y el error relativo que se cometen con esas aproximaciones. 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