How can I convert 1.19 and 0.06 to fractions while 9 and 6 are repeating decimals?

Answer 1

so you want 1.1999999 (9 repeating) into a fraction?

let A = 1.1999999
10A = 11.99999, subtract
9 A = 10.8 or
90 A = 108 so
A = 108/90 or
A = 54/45
A = 6/5.

Note that if the repeating block is 999 ... it is actually a terminating decimal!

Same thing with A = 0.0666
10A = 0.666, subtract
9 A = .6 or
90 A = 6 or
A = 6/90 or
A = 2/30 or 1/15.

Answer 2

n = 1.19999999999999999....
10n = 11.99999999999999...
subtracting,
9n = 10.8
n = 108/90 = 12/10 = 6/5

n = 0.06666666666666666....
100n = 6.66666666666666....
99n = 6.6
n = 66/990 = 22/330 = 11/165