Question

Convert the decimal expansion 0.2777... to a fraction.

Answer 1

a = 0.2777 ... = 0.2(7)

10a = 10 * 0.2(7)=2.(7)
100a = 100 * 0.2(7) = 27.(7)

100a - 10a = 27.(7) - 2.(7)
90a = 25

$a=\frac{25}{90}=\frac{5}{18}$