Question

Determine as frações geratriz: a) 0,15= b)0,555... c) -0,9999...= d) 3,7777...= e) 2,1212...= f) 0,0,125125...= g) 0,35555...= h) 0,6666....=

Answer 1

$<var>a) 0,15=\frac{15}{100}</var>$

 

 

$<var>b)0,555...=\frac{5}{9}</var>$ 

 

 

$<var>c) -0,9999...=-1</var>$ 

 

 

$<var>d) 3,7777...= 3+0,777...=3+\frac{7}{9}=\frac{34}{9}</var>$ 

 

 

$<var>e) 2,1212...=2+0,121212...=2+\frac{12}{99}=\frac{210}{99}</var>$$<var> f) 0,125125...=\frac{125}{999}</var>$ 

 

 

$<var> g) 0,35555...=\frac{3,5555...}{10}=\frac{3+0,555...}{10}=\frac{3+\frac{5}{9}}{10}=\frac{\frac{32}{9}}{10}=\frac{32}{90}</var>$ 

 

$<var>h) 0,6666....= \frac{6}{9}=\frac{2}{3}</var>$ 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

a) $<var>\frac{15}{100}</var>$

 

b) $<var>\frac{5}{9}</var>$

 

c) $<var>\frac{-9}{9}</var>$ = -1

 

d) $<var>\frac{34}{9}</var>$

 

e) $<var>\frac{210}{99}</var>$

 

f) $<var>\frac{125}{999}</var>$

 

g) $<var>\frac{32}{90}</var>$

 

h) $<var>\frac{6}{9}</var>$