Question

Ache as frações geratrizes dos números decimais abaixo e simplifique as frações.

A) 7,12424242... B) 33,199999999...

C) 0, 231231231... D) -12,6666...

Answer 1

$\Large\boxed{\begin{array}{l}\rm A)~\sf x=7,1242424\dotsc\cdot10\\\sf 10x=71,242424\dotsc\cdot100\\\sf 1000x=7124,2424\dotsc\\-\underline{\begin{cases}\sf 1000x=7124,242424\dotsc\\\sf 10x=71,2424\dotsc\end{cases}}\\\sf 990x=7053\\\\\sf x=\dfrac{7053\div3}{990\div3}\\\\\sf x=\dfrac{2351}{330}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm B)~\sf x=33,1999\dotsc\cdot10\\\sf 10x=331,999\dotsc\cdot10\\\sf 100x=3319,999\dotsc\\-\underline{\begin{cases}\sf 100x=3319,999\dotsc\\\sf 10x=331,999\dotsc\end{cases}}\\\sf 90x=2988\\\sf x=\dfrac{2998\div2}{90\div2}\\\\\sf x=\dfrac{1499}{45}\end{array}}\checkmark$

$\Large\boxed{\begin{array}{l}\rm C)~\sf x=0,231231\dotsc\cdot1000\\\sf 1000x=231,231231\dotsc\\-\underline{\begin{cases}\sf 1000x=231,231231\dotsc\\\sf x=0,231231\dotsc\end{cases}}\\\sf 999x=231\\\sf x=\dfrac{231\div3}{999\div3}\\\\\sf x=\dfrac{77}{333}\end{array}}\checkmark$

$\Large\boxed{\begin{array}{l}\rm D)~\sf x=12,666\dotsc\cdot10\\\sf 10x=126,666\dotsc\\-\underline{\begin{cases}\sf 10x=126,666\\\sf x=12,666\end{cases}}\\\sf 9x=114\\\sf x=\dfrac{114\div3}{9\div3}\\\\\sf x=\dfrac{38}{3}\\\\\sf -12,666\dotsc=-\dfrac{38}{3}\end{array}}$