Question

if x=0.7 bar and y= 0.23bar the rational number brtween x+y amd x-y is​

Answer 1

Answer:

x+y=0.7+0.23

x-y=0.7-.23

Answer 2

The rational number between x+y and x-y are $\frac{99}{99},\frac{98}{99},\frac{97}{99},....,\frac{52}{99},\frac{53}{99}$

Step-by-step explanation:

Given : If x=0.7 bar and y= 0.23bar

To find : The rational number between x+y and x-y is​ ?

Solution :

Let $x=0.777$ ....(1)

Multiply both side by 10,

$10x=7.777...$ .....(2)

Subtract (1) and (2),

$10x-x=(7.777...)-(0.777...)$

$9x=7$

$x=\frac{7}{9}$

Similarly,

Let $y=0.232323...$ ....(1)

Multiply both side by 100,

$100y=23.2323...$ .....(2)

Subtract (1) and (2),

$100y-y=(23.2323...)-(0.2323...)$

$99y=23$

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

Now, $2.3\bar6\pm0.\bar{23}=x\pmy$

i.e. $x+y=\frac{7}{9}+\frac{23}{99}$

$x+y=\frac{7\times 99+23\times 9}{9\times 99}$

$x+y=\frac{693+207}{9\times 99}$

$x+y=\frac{900}{9\times 99}$

$x+y=\frac{100}{99}$

Similarly, $x-y=\frac{7}{9}-\frac{23}{99}$

$x-y=\frac{7\times 99-23\times 9}{9\times 99}$

$x-y=\frac{693-207}{9\times 99}$

$x-y=\frac{486}{9\times 99}$

$x-y=\frac{6}{11}$

The rational number between $\frac{100}{99}$  and $\frac{6}{11}$

Multiply and divide $\frac{6}{11}$  by 9,

$\frac{6\times 9}{11\times 9}=\frac{54}{99}$

So, the rational number between $\frac{100}{99}$ and $\frac{54}{99}$ are $\frac{99}{99},\frac{98}{99},\frac{97}{99},....,\frac{52}{99},\frac{53}{99}$

#Learn more  

Express 3.42 (bar on 42) in p/q form.

https://brainly.in/question/5727549