Prove algebraically that the recurring decimal 0.35 (the 5 recurring) has the value (32)/(90)

Question

Prove algebraically that the recurring decimal 0.35 (the 5 recurring) has the value
`(32)/(90)`

Answer 1

Explanation:

r10 = 3.555555555...

r100 = 35.55555555...

then, r100-r10 = 35.555... - 3.555...

r90= 32

to find r, divide both sides by90

which will give as ;

r = 32

------

90