Express as a ratio of two numbers

0.14414414.....

Let         x = 0.144 144 144 144 ....
Let 1000x = 144. 144 144 144...

Subtract x from 1000x, you get:

999x =144


Solve for x, x = 144/999.

Check: 144/999 = .14414414.....☑check!


Answer:
0.144144144... = 144/999


See Ya!
alice

P.S.: "As a ratio of two numbers...." Other ratios could be: 16/111, 2.88/19.98, 1.777.../12.333..., etc.

0.144144144...
Repeat cycle is 3
number is written in base-10
Therefore, factor is 10^3 = 1,000

The rational fraction will look like p/q
where p and q are integers.

p/q = 0.144144144... forever
multiply both sides by 1000
1000p/q = 144.144144144... forever
subtract first from second
999p/q = 144
solve for p/q
p/q = 144/999
reduce to lowest term
16/111

x=0.14414414.....
1000x=144.14414414.....
1000x-x=999x=144

x=144/999=16/111

18018/125000

9009/62500