Question

Qual é a representação decimal de cada um dos seguintes números racionais

1/2
7/3
9/5
37/20
35/11
11/9
11/8
33/25
3/20
13/90
33/4
25/6

Answer 1

Resposta:

a)0,5        b)2,1111     c)1,8      d)1,85      e)12,3333

f)29,9165     g)3,375   h)7,48  i)8,15   j)237,0555   k)8,25    l)3,1681

Explicação passo-a-passo:

1/2=

1/1=1

10/2=5

5.2=10

1/2=(10/2): 10

=0,5

7/3=

21/3=7

21/9=2,1111

sendo o semelhante triplo 2,11111

9/5=

90=50+40=5.10+4.10=9.10

90/5=9.2=18

9/5=1,8

37/20=

37=15+15+3,5+3,5

18,5/10=1,85

35/11=

=(33+2)/11

=3 2/11

=3. (2+20)/11=3.2+20/11

=5+20/11

=5+ 20/(5+6)

=5+4+10/3

=9+3,3333

=12,3333

11/9=

(11+7)/9=2

2-7/9=

=2 - (7+2)/9

=2- 1+ 2/9

=1+ 2/9

=1+ 2/18

=1+ (1/9 . 1/2)

=1+ (9/9.1/2)

=1+ (8+1/9.1/2)

=1+{(1+8/9).1/2}

=1+[{1+(6+2)/9}.1/2]

=1+[{1+(1/3+2/9).1/2}]

=1+[{1+(  5/9).1/2}]

=1+[{1+5/18}]

=1+ [  23/18]

=1+(23+1)/18

=1+ (8/6+ 1/18)

=1+(4/3+1/18)

=1+(1/12+ 3/6)

=1+ (1+ 6 /12)

=1+ (7/12)

=1+ (6+1/12)

=1+ (1/2+ 1/12)

=1+(0,5+1+11/12)

=1+ (0,5+1+1+1/12)

=1+{0,5+2+(1+5)/12}

=1+{0,5+2+(0,5+5/12)}

=1+[2,5+{0,5+(5+1)/12}]

=1+ [2,5+{0,5+0,5+1/12}]

=1+[2,5 + {1 +1/12}]

=1+ [2,5 + 13/12]

=1+[2,5+ 24/12]

=1+[2,5+2 + 11 /12]

=1+[4,5+24/12]

=1+[4,5+2+13/12]

=1+[6,5+36/12]

=1+{6,5+(3+23/12)}

=1+{6,5+(3 + 2 + 1/12)}         1/12=5+1/12=0,5+5/12

=1+ { 6,5+ (3+2+0,5+5/12)}       5/12=3+2/12

=1+{6,5 +(5,5+1/4+1/6)}

=1+{6,5 +(5,5+0,25+16,6665)}

=1+{6,5+(5,75+16,6665)}

=1+{6,5+( 22,4165)}

=1+{28,9165}

=29,9165

11/8=

=(11+5)/8

=16/8

=2+5/8

=2+{(5+3)/8}

=2+(1+3/8)

=2+(1+2/8+ 1/8)

=2+(1+0,25+0,125)

=2+(1,375)

=3,375

33/25=

=100/25

=4+ 67/25

=4+75/25

=4+ 3+ 8/25

=7+0,2 + 3/25

=7,2+(3+2)/25

=7,2+0,2 +2/25

=7,4+0,08

=7,48

3/20=

=(57+3)/20

=60/20

=3+ 57/20

=3+ {(57+3)/20}

=3+{(60/20)}

=3+{(3+3/20)}   OBS.: 3/20 É DIFERENTE DE {(....+3/20)}

=3+{(3+3+17/20)}

=3+{(3+20/20)}

=3+{3+1+17/20)}

=3+{4+(10+7)/20}

=3+{4+(10/20+7/20)}

=3+[4+{0,5+ (7+3)/20}]

=3+[4+{0,5+0,5+3/20}]

=3+[4+{1+(2+1)/20}]    OBS.:2/20=1/10=0,1   1/20....>(1/2)(2/20)...>>0,1:2=0,05

=3+[4+{1+0,1+0,05}]

=3+[4+1,15]

=3+5,15

=8,15

13/90=

=(77+13)/90

=90/90

=1+77/90

=1+(90/90)

=1+1 +(13/90)

=2+180/90

=2+(167/90)+3

=5+(270/90)

=5+3+(103/90)

=8+(360/90)   360-103= 257

=8+4+(257/90)

=12+ (180+77/90)

=12+ 2+(77/90)

=14+(45+32/90)

=14+(45/90 + 32/90)

=14+0,5+(30+2/90)

=14,5+1/3 +2000/9   OBS.:30/90=1/3=100:3....>33,3333...>>0,3333

=14,5+ 0,3333+ 222,2222

=14,5 +222,5555      KABUM: 100:3=33,3333       2000/9=222,2222          

=237,0555

33/4=

=(28+5)/4

=7+ 5/4     OBS.: 5:4=25:20=25:2:10=12,5:10=1,25

=7+ 1,25

=8,25

25/6=

=24+1/6

=3+1/6  1/6=>100/3=33,3333 LOGO 1/6=0,16818181812181818171818180

=3+0,1681

=3,1681