Question

write 357.417417... in p/q form​

Answer 1

$\textsf{Let \ x=357.\overline{417} } \\ \\ \textsf{As a 'three digit number' is being recurred after decimal point,}\\ \textsf{we have to multiply this number (i.e., x ) by 1000} \\ \\ \\ \Longrightarrow\ 1000x=1000 \times 357.\overline{417} \\ \\ \Longrightarrow\ 1000x=357417.\overline{417} \\ \\ \\ \textsf{Now we can subtract x from 1000x }$

$\Longrightarrow\ 1000x-x=357417.\overline{417}-357.\overline{417} \\ \\ \\ \Longrightarrow\ 999x=357060 \\ \\ \\ \Longrightarrow\ x= \ \displaystyle \frac{357060}{999} \\ \\ \\ \Longrightarrow\ x=\large \textbf{ \bold{\frac{119020}{333}} }$

$\textsf{Thus, 357.\overline{417} is written as a fraction. }$

Answer 2

Answer:

11902/333

Step-by-step explanation:

let    m = 357.417417....

1000m  =357417.417417.......

now 1000m - m = 357417.417417  - 357.417417.....

      999m =357417-357

      999m= 357060

            m =35706/999=11902/333