Question

Express 2.36bar + 0.23bar as a fraction in simplest form

Answer 1

2.36 bar = 2.3636
100 x = 236.3636
100 x - x = 234
99 x = 234
x = 234/99 = 78/33 = 26/11
0.23 bar = 0.2323
100 x = 23.2323
100 x - x = 23
99 x = 23
x = 23/99
26/11+23/99=234+23/99=257/99

Answer 2

$\bold{\frac{257}{99}}$ is the fraction obtained in simplest form for the given equation   $\bold{2 . \overline{36}+0 . \overline{23}}$

Solution:  

$2 . \overline{36}$= 2.363636…..

Let x = 2.363636…..

Consider 100x = 236.3636……   (As the recurrence is for two digits we considered 100x)

100x -x = 236.3636… - 2.3636…= 234

99x = 234

x=$\frac{234}{99}$

$0 . \overline{23}$ = 0.232323….

Let x = 0.2323…

100x = 23.2323…

100x – x = 23

99x = 23

x=$\frac{23}{99}$

Therefore,$\bold{\overline{36}+0 . \overline{23}=\frac{234}{99}+\frac{23}{99}=\frac{257}{99}}$