Question

Represente os números na forma de fração irredutível:

a) 3,4

b) 1,25

c) 0,7777...

d) 0,45555....

e) 3,88888...

Answer 1

a)

$3.4=\dfrac{34}{10}=\boxed{\dfrac{17}{5}}$

b)

$1.25=\dfrac{125}{100}=\boxed{\dfrac{5}{4}}$

c)

$0.777\dots=x\ \therefore\ 7.777\dots=10x\\\\ 10x-x=7.777\dots-0.777\dots\ \therefore\ 9x=7\ \therefore\ \boxed{x=\dfrac{7}{9}}$

d)

$0.4555\dots=x\ \therefore\ 4.555\dots=10x\ \therefore\ 45.555\dots=100x\\\\ 100x-10x=45.555\dots-4.555\dots\ \therefore\ 90x=41\ \therefore\ \boxed{x=\dfrac{41}{90}}$

e)

$3.888\dots=x\ \therefore\ 38.888\dots=10x\\\\ 10x-x=38.888\dots-3.888\dots\ \therefore\ 9x=35\ \therefore\ \boxed{x=\dfrac{35}{9}}$