Question

Determine a geratriz das dízimas:

a) 0,45333....

b)0,7232323.....

c)0,8142424....

Answer 1

$a)\ 0,45333...=0,45+0,00333...=\dfrac{45}{100}+\dfrac{3}{900}=\\=\dfrac{135}{300}+\dfrac{1}{300}=\dfrac{136}{300}=\dfrac{34}{75}$

$b)\ 0,7232323...=0,7+0,0232323...=\dfrac{7}{10}+\dfrac{23}{990}=\\=\dfrac{693}{990}+\dfrac{23}{990}=\dfrac{716}{990}=\dfrac{358}{495}$

$b)\ 0,81424242...=0,81+0,00424242...=\dfrac{81}{100}+\dfrac{42}{9900}=\\=\dfrac{8019}{9900}+\dfrac{42}{9900}=\dfrac{8061}{9900}=\dfrac{2687}{3300}$