How to convert recurring decimals to common fractions

Converting recurring decimals to common fractions.

This requires a special process. Let the recurring decimal be equal to
a letter of the alphabet. Multiply both sides by 10 raised to power n,
where n is the number of recurring digits in the recurring decimal.
Subtract the first equation from the second and you will get the
fractional value of the recurring decimal.

EXAMPLES

(a) 0.111................

Solution.

R = 0.11... .............(1).
10R = 1.11... ................(2).
Subtract equation (1) from (2).
9R = 1.
R = 1/9.

(b) 0.1515................

Solution

X = 0.1515... .............(1).
100X = 15.1515... .............(2).
Subtract (1) from (2).
99X = 15.
X = 15/99 = 5/33.

(c)0.285714285714................

Solution

t = 0.285714... .............(1).
1 000 000 t = 285 714. 285714... .............(2).
Subtract (1) from (2).
999 999 t = 285 714.
t = 285 714 / 999 999 = 2/7.