Question

obtenha a fração geratriz de cada dizima periódica:
a) 3,7777...
b) 7,34444...
c) 5,126666...

Answer 1

a) iguala a X
x=3,777... ×10
10x=37,777... subtrai o de baixo pelo de cima fica
9x=34
x=34/9


b)x=7,3444... ×10
10x=73,444... ×10
100x=734,444...
90x=661
x=661/90



c)x=5,12666...×100
100x=512,666...×10
1000x=5126,666...
900x=4614
x=4614/900 simplifica por 6
x=769/150

Answer 2

Boa tarde

a)

3.777... = 3 + 0.777...

x = 0.777
10x = 7.777
9x = 7
x = 7/9 

3 + 0,777 = 3 + 7/9 = 34/9 

b) 

7.3444... = 73/10 + 0.0444..

x = 0.0444...
10x = 0,444...
100x = 4.444...
90x = 4
x = 4/90 = 2/45 

7,3444... = 73/10 + 2/45 

= (73*45 + 2*10)/450
= 3305/450 = 661/90 

c) 

5.12666... = 512/100 + 0.00666...

x = 0.00666...
1000x = 6,666...
100x = 0.666...
900x = 6
x = 6/900 = 1/150 

5.12666... = 512/100 + 1/150
= 256/50 + 1/150
= (768 + 1)/150 = 769/150