Respuesta :

Answer:

[tex]\frac{212}{99}[/tex]

Step-by-step explanation:

We require 2 equations with the repeated part after the decimal point. Then subtract them to eliminate the repeating part.

let x = 2.1414... (1) ← multiply both sides by 100

100x = 214.1414... → (2)

Subtract (1) from (2)

100x - x = 214.1414 - 2.1414, that is

99x = 212 ( divide both sides by 99 )

x = [tex]\frac{212}{99}[/tex]

That is 2.1414... = [tex]\frac{212}{99}[/tex]

Simplified fraction of 2.14(.14 being repeated) is 212/99.

What are simplified fraction?

A fraction is said to be in its simplified if the fractions in their lowest, reduced and simplest form.

Now the given fraction is 2.141414....

Let x = 2.14141414....  -------- (1)

Multiply by 100 on both sides.

100x = 214.141414....

100x = 214.141414... -------- (2)

Subtract (1) from (2),

100x - x = 214.141414... -  2.14141414....

99x = 212

Divide by 99 on both sides, we get

x = 212/99

Hence the simplified fraction is 212/99

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