MATH SOLVE

7 months ago

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

Accepted Solution

A:

◆ 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

_____[tex]x = \frac{39}{99} \\ \\ x = \frac{13}{33} \: \: \: \: \: \: \: \: \: \: \: Ans.[/tex]

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

_____[tex]x = \frac{39}{99} \\ \\ x = \frac{13}{33} \: \: \: \: \: \: \: \: \: \: \: Ans.[/tex]