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.
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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