Question

1. passe para forma de fração cada um dos seguintes decimais exatos:

a) 0,57

b) 1,28

c) 3,125

d) -31,25

e) 0,7

f) 0,718

g) 1,3147

h) 4,718365

2. escreva na forma de fração cada um dos decimais periódicos:

a) 3,22...

b) 5,4747...

c) 6,1777...

d) 2,714714...

e) 5,666...

f) 3,98111...

3. obter a geratriz das seguintes dízimas periódicas:

a) 0,444...

b) 3,888...

c) 9,1515...

d) 4,7222...

e) 8,715715...

f) 5,4317878...

8. assinale a afirmativa verdadeira:

a) 0,3100301311... € Q

b) 4,19 € Z+

c) -2,112112... € Q+

d) 4,151515 ... € R​

Answer 1

Resposta:

1)

a)

$0,57 = \green{ \dfrac{57}{100}}$

b)

$1,28 = \dfrac{128÷4}{100÷4} \\\ \\\green{\dfrac{32}{25}}$

c)

$3,125 = \dfrac{3125÷125}{1000÷125}\\\\ \green{\dfrac{25}{8}}$

d)

$- 31,25 = - \dfrac{3125÷25}{100÷25} \\\\\green{-\dfrac{125}{4}}$

e)

$0,7 = \green{ \dfrac{7}{10}}$

f)

$0,718 = \dfrac{718÷2}{1000÷2}\\\\ \green{\dfrac{359}{500} }$

g)

$1,3147 = \green{ \dfrac{13147}{10000}}$

h)

$4,718365 = \dfrac{4718365 \div 5}{1000 \: 000 \div 5} \\ \\ \green{\dfrac{943673}{200 \: 000} }$

2)

a)

$3,22... = 3 + \dfrac{22}{99} = \dfrac{3 \times 99 + 22}{99} = \green{\dfrac{319}{99} }$

b)

$5,4747... = 5 + \dfrac{47}{99} = \dfrac{5 \times 99 + 47}{99} = \green{\dfrac{542}{99} }$

c)

$6,1777... = 6 + \dfrac{17 - 1}{90} = \dfrac{6 \times 90 + 16}{90} = \dfrac{556 \div 2}{90 \div 2} = \\ \\ \dfrac{278}{45}$

d)

$2,714714... = 2 + \dfrac{714}{999} = \dfrac{2 \times 999 + 714}{999} = \\ \\ \dfrac{2712 \div 3}{999 \div 3} = \dfrac{904}{333}$

e)

$5,666... = 5 + \dfrac{6}{9} = \dfrac{5×9 + 6}{9} =\green{ \dfrac{51}{9} }$

f)

$3,98111... = 3 + \dfrac{981 - 98}{900} = 3 + \dfrac{883}{900} = \\ \\ \dfrac{3 \times900 + 883}{900} = \dfrac{3583}{900}$

3)

a)

$0,444 ... = \dfrac{4}{9}$

b)

$3,888... = 3 + \dfrac{8}{9} = \dfrac{3 \times 9 + 8}{9} = \dfrac{35}{9}$

c)

$9,1515... = 9 + \dfrac{15}{99} = \dfrac{9 \times 99 + 15}{99} = \dfrac{906}{99}$

d)

$4,7222... = 4 + \dfrac{72 - 7}{90} = \dfrac{4 \times 90 + 65}{90} = \\ \\ \dfrac{425 \div 5}{90 \div 5} = \dfrac{85}{18}$

e)

$8,715715... = 8 + \dfrac{715}{999} = \dfrac{8 \times 999 + 715}{999} = \dfrac{8707}{999}$

f)

$5,4317878... = 5 + \dfrac{43178 - 431}{99000} = \\ \\ \dfrac{5 \times 99000 + 42747}{99000} = \dfrac{537747}{99000}$

4)

Sequêcia:

--- 1,1 -1,2 - 1,25 - 1,3 - 1,35 - 1,4 - 1,45 - 1,5 - 1,55 - 1,6 - 1,65 - 1,7 - 1,75 - 1,8 - 1,9 ----

5)

a)

$2 > - 3$

b)

$- 3 > - 5$

c)

$\dfrac{3}{5} > \dfrac{7}{5}$

d)

$- \dfrac{2}{7} > - \dfrac{3}{7}$

e)

$- \dfrac{5}{11} < \dfrac{8}{11}$

f)

$0,75 < 0,77$

g)

$2,98 > 2,957$

h)

$0,71 < \dfrac{71}{99}$

i)

$- 0,833 > - 0,83411$

j)

$( - 0,333...) = - \dfrac{1}{3}$

k)

$1,25 > (1,2345678...)$

l)

$( - 1,234567...) > - 1,235$

6)

Sequência crescente:

0,6 ; 0,626262... ; 2/3 ; 0,6789101112...

$\green{0,6 - 0,626262... - \frac{2}{3} - 0,6789101112...}$

7)

$\dfrac{1}{4} = 0,24 \\ \\ \frac{2}{7} \cong0,28 \\ \\ \frac{3}{13} \cong0,23 \\ \\ \green{\dfrac{3}{13} < \dfrac{1}{4} < \dfrac{2}{7} }$

Bons Estudos!