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
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?
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?