text: show reapeating decimals as fraction in infinite geometric series? f0rmula: (t1) ---- 1-r  reads: (t1) divided by (1-r) t1 is first number. r is ratio of geometric series  1) 9.345345345 2) -66.9323232...  first write in geometric series then use formula. show work  answer for 1: 3112/333 answer for 2: -66263/990 1) 9.345345 = 9 + 0.345 + 0.000345 + ... = 9 + (345)10^-3 + (345)10^-6 + ... = 9 + 345*sum(i=1 to inf) 10^(-3i) = 9 + 345*sum(i=1 to inf) (10^3)^(-i) = 9 + 345*sum(i=1 to inf) (1/1000)^i = 9 + 345(1/1000/(1-1/1000)) = 9 + 345(1/999) = 9 + 115/333 = 2997/333 + 115/333 = 3112/333  b) -66.93232... = -66.9 - 0.032 - 0.00032 - ... = -66.9 - (32)10^-3 - (32)10^-5 - (32)10^-7 - ... = -66.9 - 32*sum(i=1 to inf) 10^(-2i-1) = -66.9 - 32*sum(i=1 to inf) (10^2)^-i*10^-1 = -66.9 - (32/10)sum(i=1 to inf) (1/100)^i = -66.9 - (32/10)(1/100/(1-1/100)) = -66.9 - (32/10)(1/99) = -669/10 - 32/990 = -66231/990 - 32/990 = -66263/990