x = 0.045 (45 recurring). Prove algebraically that x can be written as 1/22

x=0.045 (45 recurring)

10x = 0.45 (45 recurring)

100x = 4.54 (54 recurring)

1000x = 45.45 (45 recurring)

To get rid of the decimals:

1000x-10x = 45.45 - 0.45

990x = 45

x = 45/990

x = 9/198 (simplify by dividing by 5)

x = 1/22 (simplify by dividing 9)