Question

Express each of the following in form of p/q (a) 3.23 bar on 23


(b) 0.23 bar on 3

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$\bf 3.\overline{23}$

Let x = 3.232323.....  ___(i)

Multiplying 100 to both side of equation (i), we get

100x = 323.232323....  ___(ii)

Now,

subtracting equation (i) from equation (ii), we get

 

100x = 323.232323....

-     x =     3.232323.....

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  99x = 320.00000...

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⇒ 99x = 320

⇒ x = 320 ÷ 99

$\therefore \bf x = \frac{320}{99}$

________________________

$\bf 0.2\overline{3}$

Let x = 0.23333.....  ___(i)

Multiplying 10 to both side of equation (i), we get

10x = 2.3333....  ___(ii)

Multiplying 10 to both side of equation (ii), we get

100x = 23.3333....  ___(iii)

Now,

subtracting equation (ii) from equation (iii), we get

 

100x = 23.33333....

- 10x =    2.33333.....

------------------------------------

 90x = 21.00000....

------------------------------------

⇒ 90x = 21

⇒ x = 21 ÷ 90

$\therefore \bf x = \frac{21}{90}$