Question

Express 1.16bar as a rational no. In the simplest form

Answer 1

let us take X=1.16 bar
now 100X=116.16bar
subtract 100X-X
100X-X= 116.1616 - 1.1616
99X= 115
X= 115/99
your ans is 115/99

HOPE IT HELPS YOU!

Answer 2

Let x = 1.$\bar{16}$

As there are two numbers under bar, multiply by 100 on both sides,

⇒ 100 × x = 100 × 1.$\bar{16}$

⇒ 100x = 116.$\bar{16}$

Now, subtract x both from both sides of the equation formed above.

100x = 116.$\bar{16}$

-    x =   -1.$\bar{16}$

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 99x =  115 [ bar cancelled ]

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$\implies 99x = 115 \\\\ \implies x = \dfrac{115}{99}$

From above, x = 1.$\bar{16}$

$\therefore 1.\bar{16} = \dfrac{115}{99}$

Hence, 1.$\bold{\bar{16}}$ as a rational number in simplest form is $\dfrac{115}{99}$