Question

Express the number as a ratio of integers. 0.39 = 0.39393939

Answer 1

◆ NUMBER SYSTEMS ◆

Let 0.393939... = x
Or , x = 0.393939... ---eq.(1)

Multiplying both sides by 100

We get ,
_____ 100x = 39.393939... --- eq.(2)

Subtracting eq.(1) from eq.(2)

We get ,
100x-x = 39.393939... - 0.393939...
_____ 99x = 39

_____$x = \frac{39}{99} \\ \\ x = \frac{13}{33} \: \: \: \: \: \: \: \: \: \: \: Ans.$