Recognizable Fractions

Algebra Level 1

$\large {0.\overline{6}} \ +{0.\overline{3}} \ = \, ?$

Note : $0.\overline{a} \ = \ 0. aaaa\ldots$

1 0.9

0.\overline{3}

3 solutions

Atul Shivam
Jan 13, 2016

let $x=0.6666.....$ and $y=0.3333.....$

$10x=6.6666.....$ now $10x-x=6.6666.... - 0.6666.....$ so $x=\frac{6}{9}$ similarly $y=\frac{3}{9}$

now we have to find $x+y$ which is $\frac{6}{9}+\frac{3}{9}\ =\boxed {1}$

Manisha Garg
Jan 15, 2016

0.666 ... + 0.3333 ...

= 0.9999 ....

x = 0.999 ....

10x = 9.9999 ...

9x = 9.9999... - 0.9999... = 9

x = 1 Hence, ans is $\boxed{ 1 }$

Rishabh Jain
Jan 13, 2016

Let x=0.6666....+0.3333......= 0.9999..... 10x=9.9999......

Subtracting, we get 9x=9 or x= $\color{magenta}{1}$

you cannot directly add $0.666....+0.333....$ then you will get value of $x=0.999....$ which is also one of the option

Atul Shivam - 5 years, 5 months ago

Both C and D are correct!!

Rishabh Jain - 5 years, 5 months ago

There are 2 correct answers. That's why many people including me have reported.

Kushagra Sahni - 5 years, 5 months ago

yes!!! but can I make a report on any problem which I have solved and found correct

Atul Shivam - 5 years, 5 months ago

@Atul Shivam – Yes, even I did that.

Kushagra Sahni - 5 years, 5 months ago