Change repeating decimal to fraction

Please help to solve:

0.143 (3 repeating) I solved the following way:

x=0.143 (3 repeating)

100x=14.3 (3 repeating)

1000x= 143.3 (3 repeting)

1000x - 100x = 143.3-14.3

900x = 129

x= 129/900

My question: how to solve this problem using geometric series?

14/100 + 0.003 (3 repeating)

I guess we need to find fraction for 0.003 (3 reapeting)

What is the first term? What is the common ratio?

Please help.

Thanks

Use Pascal's Triangle and expand

(2x-3)^4 = 16x^4-96x^3+216x^2-216x + 81

Is this correct? I did it using binomial theorem, why do I need to use Pascal's triangle?

Thank you