Work out recurring decimal to fraction instantly with clear inputs, formula shown and shareable results.
For a decimal 0.a(b) with p non-repeating digits and q repeating digits, multiplying by 10^(p+q) and by 10^p and subtracting eliminates the tail, giving (ab − a) / (10^p(10^q − 1)).
Recurring decimal
0.a(b) = (ab − a) / (10^p · (10^q − 1)), p = length of a, q = length of b
With a = 1 and b = 6: (16 − 1)/(10 × 9) = 15/90 = 1/6.
With no non-repeating digits and b = 9: (9 − 0)/9 = 1. Recurring nine really does equal one.