Question

Q.1 The value of 1.3 bar on 3 + 0.123 bar on 23-0.11 bar on 11 is equal to:​

Answer 1

Given:  1.3 bar on 3  +  0.123 bar on 23-0.11 bar on 11

$1.\overline{3}+0.1\overline{23}-0.\overline{11}$

To Find: Value

Solution:

$1.\overline{3}+0.1\overline{23}-0.\overline{11}$

$a=1.\overline{3}$

$b=0.1\overline{23}$

$c=0.\overline{11}$

a + b - c

$a=1.\overline{3}$

$10a=13.\overline{3}$

=> 9a = 12

=> a = 4/3

$b=0.1\overline{23}$

$10b=1.\overline{23}$

$1000b=123.\overline{23}$

=> 990b = 122

=> b = 122/990

=> b = 61/495

$c=0.\overline{11}$

$100c=11.\overline{11}$

=> 99c = 11

=> c = 1/9

4/3 + 61/495 - 1/9

= ( 660 + 61 - 55)

= 666/495

= 222/165

= 74/55

= $1.3\overline{45}$

$1.\overline{3}+0.1\overline{23}-0.\overline{11}$ = $1.3\overline{45}$  = 74/55

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