Question

Express 0.47777……. as p/q.​

Answer 1

$\LARGE\star\mathfrak{\underline{\underline{\red{answer: }}}}$

$\sf{0.47777... \: can \: be \: written \: as \: 0.4 \bar7}$

$\sf{let \: x = 0.4 \bar7} \: \: \: \: \: \: \: \: \: \: \: \: ...(1) \\ \sf{multiply \: by \: 10 \: both \: sides} \\ \sf{10x = 4. \bar7} \: \: \: \: \: \: \: \: \: \: \: \: ...(2) \\ \sf{now \: multiply \: by \: 100 \: in \: both \: sides \: in \: eq \: (1)} \\ \sf{100x = 47. \bar7 \: \: \: \: \: \: \: \: ...(3)} \\ \sf{subtract \: eq(2) \: from \: eq(3)} \\ \sf{100x - 10x = 47. \bar7 - 4. \bar7} \\ \sf{90x = 43} \\ \boxed{\sf{x = \frac{43}{90} }}</p><p>$