Question

Express 2.36bar (bar is only for 6) ±0.23bar as a fraction in simplest form

Answer 1

2.364+0.232
2364/1000+232/1000
1284/500+116/500
642/250+58/250
321/125+29/125
350/125
70/25
14/5

Answer 2

Answer:

$2.3\bar6\pm0.\bar{23}=\frac{2573}{990},\frac{2113}{990}$

Step-by-step explanation:

Given : Expression $2.3\bar6\pm0.\bar{23}$

To find : Express expression as a fraction in simplest form?

Solution :

Let $x=2.36666$ ....(1)

Multiply both side by 10,

$10x=23.666...$ .....(2)

Subtract (1) and (2),

$10x-x=(23.666...)-(23.666...)$

$9x=21.3$

$x=\frac{21.3}{9}$

$x=\frac{213}{90}$

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. $x+y=\frac{213}{90}+\frac{23}{99}$

$x+y=\frac{213\times 99+23\times 90}{90\times 99}$

$x+y=\frac{21087+2070}{90\times 99}$

$x+y=\frac{23157}{90\times 99}$

$x+y=\frac{2573}{990}$

Similarly, $x-y=\frac{213}{90}-\frac{23}{99}$

$x-y=\frac{213\times 99-23\times 90}{90\times 99}$

$x-y=\frac{21087-2070}{90\times 99}$

$x-y=\frac{19017}{90\times 99}$

$x-y=\frac{2113}{990}$

Therefore, $2.3\bar6\pm0.\bar{23}=\frac{2573}{990},\frac{2113}{990}$