Question

Simplify : 0.3434...+0.696969....+0.8080-0.4444...-0.3333....-0.07070...​

Answer 1

Answer:

0.34+0.69+0.80-0.4-0.3-0.7

0.43 answer

Answer 2

Answer:

$1.$

Step-by-step explanation:

Given,

$0.3434...+0.696969...+0.8080...-0.4444...-0.3333...-0.07070...$

Let $x=0.3434...$  This is our first equation.

then $100x=34.3434...$ This is our second equation.

$100x-x=34.3434...-0.3434...$

       $99x=34$

          $x=\frac{34}{99}$

Similarly,

$0.6969...=\frac{69}{99}$

$0.8080...=\frac{80}{99}$

$0.4444...=\frac{44}{99}$

$0.3333...=\frac{33}{99}$

$0.07070..=\frac{7}{99}$

$\frac{(34+69+80-44-33-7)}{99} =\frac{99}{99} =1.$