# Fraction

Fraction
$\dfrac{0,\overline{ 40 }}{0,40 }$
write as fraction a/b, a, b is integers numerator/denominator.

Result

a =  100
b =  99

#### Solution:

$x = \dfrac{0,\overline{ 40 }}{0,40 } = \dfrac{1 }{0,40} \dfrac{ a_1}{1-q} = \dfrac{1 }{0,40} \dfrac{0,40}{1-\dfrac{1}{100}} \ \\ x = \dfrac{1}{1-\dfrac{1}{100}} = \dfrac{100}{99} \ \\$
$b=99$

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