Question

The value of $2.6\overline{34}+0.1\overline{7}$ is

• A. $2\frac{804}{999}$
• B. $2\frac{731}{990}$
• C. $2\frac{804}{990}$
• D. $2\frac{731}{9900}$

Answer 1

Answer: (C)

$2\frac{804}{990}$

Given, $2.6\overline{34}+0.1\overline{7}$
Converting into fraction $2.6\overline{34}$
Let $x=\mathrm{2.6343434...}$
$=>10x=\mathrm{26.343434....}$--------(i)
$=>1000x=\mathrm{2634.34343...}$----(ii)
(ii)-(i)
$=>990x=2608$
$=>x=\frac{2608}{990}$
Now Converting into fraction $0.1\overline{7}$
Let $x=\mathrm{0.17777.....}$
$=>10x=\mathrm{1.77777....}$------(i)
$=>100x=\mathrm{17.7777...}$-----(ii)
(ii)-(i)
$=>90x=16$
$=>x=\frac{16}{90}$

Now $2.6\overline{34}+0.1\overline{7}$

$=\frac{2608}{990}+\frac{16}{90}$

$=\frac{2608+176}{990}$

$=\frac{2784}{990}$

$=2\frac{804}{990}$