Question

Помогите 3,(15)х=3,1(51)

Answer 1

Ответ:

$3,(15)\, x=3,1(51)\\\\1)\ \ a=3,(15)\\\\ 100a=315,(15)\\\\100a-a=315,(15)-3,(15)\\\\99a=312\ \ ,\ \ \ a=\dfrac{312}{99}\\\\2)\ \ b=3,1(51)\\\\10b=31,(51)\\\\1000b=3151,(51)\\\\1000b-10b=3151,(51)-31,(51)\\\\990\, b=3120\ \ ,\ \ \ b=\dfrac{3120}{990}=\dfrac{312}{99}\\\\\\\dfrac{312}{99}\, x=\dfrac{312}{99}\ \ \ ,\ \ \ x=\dfrac{312}{99}\cdot \dfrac{99}{312}\ \ \ \ ,\ \ \ \ \boxed {\ x=1\ }$