Question

Express 0.87 bar + 0.6 bar in the p/q form, q ≠ 0.

Answer 1

0.87bar = 87/99
.6bar = 6/9
then 0.87 + 0.6bar
= 131/99

Answer 2

Answer:

$\frac{51}{33}$

Step-by-step explanation:

Let,

$x=0.\overline{87}$

$\implies x = 0.87878787......$ ------(1)

By multiplying 100 on both sides,

$100x = 87.8787878......$ --------(2),

Equation (2) - Equation (1),

$99x = 87$

$x=\frac{87}{99}$

Thus,

$0.\overline{87}=\frac{87}{99}$

Now, Let,

$y=0.\overline{6}$

$\implies x = 0.6666666......$ ------(3)

By multiplying 10 on both sides,

$10x = 6.666666......$ --------(4),

Equation (4) - Equation (3),

$9x = 6$

$x=\frac{6}{9}$

Thus,

$0.\overline{6}=\frac{6}{9}$

Hence,

$0.\overline{87}+0.\overline{6}=\frac{87}{99}+\frac{6}{9}=\frac{87+66}{99}=\frac{153}{99}=\frac{51}{33}$