lgebra

Unidad 1. Nmeros reales

Ciencias Exactas, Ingenieras y Tecnologa | Logstica y Transporte 1

Actividad 1. Conversin de bases y operaciones

Indicaciones: Lee detenidamente y contesta lo que te pide.

1. Expresa los siguientes nmeros (base 10) en notacin expandida:

a) 238= (2*100)+(3*10)+(8*1)

=(2*10^2)+(3*10^1)+(8*10^0)

b) 495,451= (4*100,000)+(9*10,000)+(5*1,000)+(4*100)+(5*10)+(1*1)

= (4*10^5)+(9*10^4)+(5+10^3)+(4*10^2)+(5*10^1)(1*10^0)

c) 476,433= (4*100,000)+(7*10,000)+(6*1,000)+(4*100)+(3*10)+(3*1)

=(4*10^5)+(7*10^4)+(6*10^3)+(4*10^2)+(3*10^1)+(3*10^0)

d) 257,988= (2*100,000)+(5*10,000)+(7*1,000)+(9*100)+(8*10)+(8*1)

=(2*10^5)+(5*10^4)+(7*10^3)+(9*10^2)+(8*10^1)+(8*10^0)

e) 19,018 = (1*10,000)+(9*1,000)+(1*10)+(8*1)

=(1*10^4)+(9*10^3)+(1*10^1)+(8*10^0)

f) 279,456 = (2*100,000)+(7*10,000)+(9*1,000)+(4*100)+(5*10)+(6*1)

=(2*10^5)+(7*10^4)+(9*10^3)+(4*10^2)+(5*10^1)+(6*10^0)

g) 492,406 = (4*100,000)+(9*10,000)+(2*1,000)+(4*100)+(6*1)

=(4*10^5)+(9*10^4)+(2*10^3)+(4*10^2)+(6*10^0)

h) 457,402= (4*100,000)+(5*10,000)+(7*1,000)+(4*100)+(2*1)

=(4*10^5)+(5*10^4)+(7*10^3)+(4*10^2)+(2*10^0)

2. Escribe los siguientes nmeros en notacin decimal:

a) (3 105) + (8 104) + (6 103) + (1 102) + (4 101)

(300,000)+(80,000)+(6,000)+(100)+(4)= 386,614

b) (2 105) + (5 104) + (1 103) + (8 102) + (5 101) + (8 100)

=(200,000)+(50,000)+(1,000)+(800)+(50)+(8) = 251,858

c) (2 105) + (3 104) + (4 103) + (9 102) + (8 101) + (3 100)

lgebra

Unidad 1. Nmeros reales

Ciencias Exactas, Ingenieras y Tecnologa | Logstica y Transporte 2

=(200,000)+(30,000)+(4,000)+(900)+(80)+(3) = 234,983

d) (8 104) + (4 103) + (1 102) + (5 101) + (6 100)

=(80,000)+(4,000)+(100)+(50)+(6) = 84,156

3. Escribe los siguientes nmeros que estn en notacin decimal en la base indicada para cada caso:

a) 1,247 a base 14=

= 651 = (6*14^2)+(5*14^1)+(1*14^0)= 1,176+70+1= 1,247

b) 2,341 a base 11

= 1,839= (1*11^3)+(8*11^2)+(3*11^1)+(9*11^0)= 1,331+968+33+9=2,341

c) 1,247 a base 4

= 103,133 = (1*4^5)+(0*4^4)+(3*4^3)+(1*4^2)+(3*4)^+(3*4^0)=1,247

d) 2,341 a base 6

= 14,501= (1*6^4)+(4*6^3)+(5*6^2)+(0*6^1)+(1*6^0)= 2,341

4. Escribe cada nmero en notacin decimal:

a) 345 = (3*5^1)+(4*5^0)= 15+4= 19

b) 3307 = (3*7^2)+(3*7^1)+(0*7^0)= 147+21= 168

c) 458 = (4*8^1)+(5*8^0)= 32+5= 37

d) 2A012 = (2*12^2)+(A*12^1)+(0*12^0)=288+120+0= 408

e) 2,0134 = (2*4^3)+(0*4^2)+(1*4^1)+(3*4^0)= 128+0+4+3= 135

f) 3,2106 = (3*6^3)+(2*6^2)+(1*6^1)+(0*6^0)= 648+72+6+0= 726

g) 3447 = (3*7^2)+(4*7)^+(4*7^0)= 147+28+4= 179

h) 9,15411 = (9*11^3)+(1*11^2)+(5*11^1)+(4*11^0)= 11,979+121+55+4= 12,159

5. Escribe cada nmero en la base indicada:

a) 345 en base 8 =(3*8^1)+(4*8^0)=15+4= 1910

238 = (2*8^1)+(3*8^0)=16+3= 1910

b) 3447 en base 6 =(3*7^2)+(4*7^1)+(4*7^0)= 147+28+4= 17910

4556= (4*6^2)+(5*6^1)+(5*6^0)= 144+30+5= 17910

lgebra

Unidad 1. Nmeros reales

Ciencias Exactas, Ingenieras y Tecnologa | Logstica y Transporte 3

c) 3,2106 en base 11 =(3*6^3)+(2*6^2)+(1*6^1)+(0*6^2)= 648+72+6+0= 72610

60011= (6*11^2)+(0*11^1)+(0*11^0)= 72610

6. Encuentra una regla para determinar si un nmero en base 9 menor a 1000,0009 es divisible entre 3.

= 999,999a + a + 99,999b + b + 9,999c + c + 999d + d + 99e + e + 9f + f 3 3 3 3 3 3 3 3 3 3 3 3

= 333,333a+33,333b+3,333c+333d+33e+3f + a+b+c+d+e+f

3

El resultado de N/3 ser entero si la suma del quebrado final es divisible entre 3 (entero).