#2**+2 **

We don't need to worry about the "5" part, yet

1) Take 228 and subtract the non-repeating part of the decimal = 228- 22 = 206....this is our numerator

2) In the denominator, write the same number of 9's as the repeating part of the decimal= 9

And write the same number of 0's as the non-repeating part of the decimal = 00

So .228 (8 repeating) = 206 / 900 = 103 / 450

So we have

5 + 103 / 450 = 2343 / 450

CPhill Feb 24, 2022

#3**+2 **

Here is another method :

x = 5.228

100x = 522.8888.....

1000x = 5228.8888.....

1000x - 100x = 900x = 5228.8888.... - 522.8888.... = 4706

900x = 4706

x = 4706/900 simplify as needed (= 5 103/450)

ElectricPavlov Feb 24, 2022