Question

A)9,22444
B)4,34242
C)5,2999
D)13,888
E)10,311414

Answer 1

Olá Raissa

a) 9.22444...

y = 9.22444... = 9 + 22/100 + 0.00444...

x = 0.00444...

100x = 0.444...
1000x = 4.444...
900x = 4 
x = 4/900 

y = 9 + 22/100 + 4/900
y = (9*900 + 22*9 + 4)/900 
y = 8302/900 
y = 4151/450 

b) 4.3424242...

y = 4.34424242 = 4 + 34/100 + 0.00424242...

x = 0.00424242...

100x = 0.424242...
10000x = 42.424242... 
9900x = 42
x = 42/9900 = 7/1650 

y = 4 + 34/100 + 7/1650 
y = 3584/825 

c) 5.2999...

y = 5 + 2/10 + 0.0999... 
y = 5 + 2/10 + 1/10 
y = 50/10 + 2/10 + 1/10
y = 53/10 

d) 13.888...

y = 13.888... = 13 + 8/9 = 
y = 125/9

e) 10.31141414...

y = 10 + 31/100 + 0.00141414... 

x = 0.00141414... = 7/4950 

y = 10 + 31/100 + 7/4950 
y = 102083/9900 

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