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◆ 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]

The number 0.39393939 expressed as a ratio of integers is;

39/99

  • We want to express 0.39393939 as a ratio of integers. That means denominator and numerator must be integers. Integers are whole numbers.

Let y = 0.39393939  ----(eq 1)

Multiply both sides by 100 to yield

100y = 39.39393939 ----(eq 2)

Subtract (eq 1) from eq(2) to yield

100y - y = 39.39393939 - 39393939

99y = 39

Using division property of equality, divide both sides by 99 to get;

99y/99 = 39/99

y = 39/99

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